Statistical Technique For Interpreting And Reporting Quantitative Data

 

Learning outcome

The learning outcome of using statistical tools can be significant, depending on the context and application. Here are some potential benefits:

Analytical Skills

1. Data analysis: Statistical tools enable individuals to collect, analyze, and interpret data, making informed decisions.

2. Pattern recognition: Statistical techniques help identify patterns and trends in data, facilitating predictive modeling and forecasting.

3. Hypothesis testing: Statistical tools allow individuals to test hypotheses and validate assumptions, ensuring data-driven decision-making.

Problem-Solving

1. Identifying correlations: Statistical tools help identify relationships between variables, enabling individuals to understand complex systems.

2. Predictive modeling: Statistical techniques enable individuals to build predictive models, forecasting outcomes and optimizing processes.

3. Quality control: Statistical tools facilitate quality control, ensuring products or services meet specified standards.

Decision-Making

1. Informed decision-making: Statistical tools provide insights, enabling individuals to make informed decisions based on data.

2. Risk assessment: Statistical techniques help assess risks and uncertainties, facilitating informed decision-making.

3. Evaluation of effectiveness: Statistical tools enable individuals to evaluate the effectiveness of interventions or programs.

Other Benefits

1. Improved critical thinking: Statistical tools promote critical thinking, enabling individuals to evaluate evidence and arguments.

2. Enhanced research skills: Statistical techniques are essential for research, enabling individuals to design studies, collect data, and analyze results.

3. Better communication: Statistical tools facilitate effective communication of complex data insights, enabling individuals to convey findings to various stakeholders.

Some common statistical tools include:

1. Descriptive statistics(e.g., mean, median, mode)

2. Inferential statistics (e.g., hypothesis testing, confidence intervals)

3. Regression analysis

4. Time series analysis

5. Data visualization tools(e.g., plots, charts)

Statistical technique for interpreting and reporting quantitative data

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it a mathematical discipline to collect, summarize data. Statistics is simply defined as the study and manipulation of data. Also, we can say that statistics is a branch of applied mathematics. However, there are two important and basic ideas involved in statistics; they are uncertainty and variation. The uncertainty and variation in different fields can be determined only through statistical analysis. These uncertainties are basically determined by the probability that plays an important role in statistics.

 Definitions of statistics given by different authors.

According to Merriam-Webster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.

According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.

Examples : Some of the real-life examples of statistics are:

 To find the mean of the marks obtained by each student in the class whose strength is 50. The average value here is the statistics of the marks obtained.

 Suppose you need to find how many members are employed in a city. Since the city is populated with 15 lakh people, hence we will take a survey here for 1000 people (sample). Based on that, we will create the data, which is the statistic.

Basics of Statistics

The basics of statistics include the measure of central tendency and the measure of dispersion. The central tendencies are mean, median and mode and dispersions comprise variance and standard deviation.

Mean is the average of the observations. Median is the central value when observations are arranged in order. The mode determines the most frequent observations in a data set.

Variation is the measure of spread out of the collection of data. Standard deviation is the measure of the dispersion of data from the mean. The square of standard deviation is equal to the variance.

Types of Statistics

Basically, there are two types of statistics.

 Descriptive Statistics

 Inferential Statistics

In the case of descriptive statistics, the data or collection of data is described in summary. But in the case of inferential stats, it is used to explain the descriptive one. Both these types have been used on large scale.

 Descriptive Statistics

The data is summarised and explained in descriptive statistics. The summarization is done from a population sample utilising several factors such as mean and standard deviation. Descriptive statistics is a way of organising, representing, and explaining a set of data using charts, graphs, and summary measures. Histograms, pie charts, bars, and scatter plots are common ways to summarise data and present it in tables or graphs. Descriptive statistics are just that: descriptive. They don’t need to be normalised beyond the data they collect.

 Inferential Statistics

We attempt to interpret the meaning of descriptive statistics using inferential statistics. We utilise inferential statistics to convey the meaning of the collected data after it has been collected, evaluated, and summarised. The probability principle is used in inferential statistics to determine if patterns found in a study sample may be extrapolated to the wider population from which the sample was drawn. Inferential statistics are used to test hypotheses and study correlations between variables, and they can also be used to predict population sizes. Inferential statistics are used to derive conclusions and inferences from samples, i.e. to create accurate generalisations.

Scope of Statistics

Statistics is used in many sectors such as psychology, geology, sociology, weather forecasting, probability and much more. The goal of statistics is to gain understanding from the data, it focuses on applications, and hence, it is distinctively considered as a mathematical science.

Methods in Statistics

The methods involve collecting, summarizing, analysing, and interpreting variable numerical data. Here some of the methods are provided below.

 Data collection

 Data summarization

 Statistical analysis

What is Data in Statistics?

Data is a collection of facts, such as numbers, words, measurements, observations etc.

Types of Data

 Qualitative data- it is descriptive data.

 Example- She can run fast, He is thin.

 Quantitative data- it is numerical information.

 Example- An Octopus is an Eight legged creature.

Types of quantitative data

 Discrete data- has a particular fixed value. It can be counted

 Continuous data- is not fixed but has a range of data. It can be measured.

Representation of Data

There are different ways to represent data such as through graphs, charts or tables. The general representation of statistical data are:

 Bar Graph

 Pie Chart

 Line Graph

 Pictograph

 Histogram

 Frequency Distribution

Bar Graph

A Bar Graph represents grouped data with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally.

Pie Chart

A type of graph in which a circle is divided into Sectors. Each of these sectors represents a proportion of the whole.

Line graph

The line chart is represented by a series of data points connected with a straight line.

The series of data points are called ‘markers.’

Pictograph

A pictorial symbol for a word or phrase, i.e. showing data with the help of pictures. Such as Apple, Banana & Cherry can have different numbers, and it is just a representation of data.

Histogram

A diagram is consisting of rectangles. Whose area is proportional to the frequency of a variable and whose width is equal to the class interval.

Frequency Distribution

The frequency of a data value is often represented by “f.” A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.

Frequency Distribution

Frequency distribution is a systematic arrangement of raw measures in to class revealing the frequencies of measures in each class.

Procedure for framing Frequency Distribution

•  Determine the highest and lowest measure.
•  Find the range, which is the difference between highest score and lowest score
•  Deciding the number of classes
•  Find the class interval
•  Starting the class interval at a value which is a multiple of size of that interval
•  Writing classes from bottom to top. Here care should be taken to include the lowest measure in lowest class and highest measure in highest class.
•  Representing each measure by using a tally mark.
•  Add the tally mark and write it numerically.
•  Find the total number of measures

Inclusive Class Interval:

 When the lower and the upper class limit is included, then it is an inclusive class interval. For example – 220 – 234, 235 – 249 ..... etc. Are inclusive type of class intervals. Usually in the case of discrete variant, inclusive type of class intervals are used.

Exclusive Class Interval:

When the lower limit is included, but the upper limit is excluded, then it is an exclusive class interval. For example – 150 – 153, 153 – 156.....etc are exclusive type of class intervals. In the class interval 150 – 153, 150 is included but 153 is excluded.

Usually in the case of continuous variate, exclusive type of class intervals are used.

Conversion of Inclusive Series into Exclusive Series

While analysing a frequency distribution, if there are inclusive type of class intervals they must be converted into exclusive type.

For statistical calculation, sometimes it becomes necessary to convert the inclusive series into exclusive series. Suppose, in the above example some students have obtained marks such as 10.5, 40,5, etc. In this case, this series will be converted into exclusive series,

The steps for converting an inclusive series into exclusive series are:

•  In this first step, calculate the difference between the upper class limit of one class interval and the lower limit of the next class interval.
•  The next step is to divide the difference by two and then add the resulting value to the upper limit of every class interval and subtract it from the lower limit of every class interval.

Example:

The inclusive series of the above example is converted into exclusive series as under.

Measures of Central Tendency

The concepts average (average mark of the pupil, an average height or weight of the pupils, an average income of the family and etc.) indicates a single value which is the outcome of the total measure. The above typical measures indicate that the values in the data concentrate at the centre or somewhere in the middle of the distribution. Such measures are called measures of central tendency. Tendency of occurrence somewhere in the middle. Here, you are representing the performance of the group as a whole by the single measure and enable you to compare two or more groups in terms of their performance. It describes the characteristics of the given data. Of the many averages, three have been selected as the most useful methods in educational research. They are the mean, median and mode.

In Mathematics, statistics are used to describe the central tendencies of the grouped and ungrouped data. The three measures of central tendency are:

1.  Mean
2.  Median
3.  Mode

All three measures of central tendency are used to find the central value of the set of data.

MEAN

Mean is an essential concept in mathematics and statistics. The mean is the average or the most common value in a collection of numbers.

In statistics, it is a measure of central tendency of a probability distribution along median and mode. It is also referred to as an expected value.

Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection. It is calculated in the following way:

Mean for a Frequency Distribution

Mean = (sum (xf))/n

Where,

F=frequency of each class

X = Mean point of each class[(lower limit+ Upper limit)/2]

n = Total frequency

Merits of Arithmetic Mean

•  Arithmetic mean is rigidly defined
•  It is easy to calculate and simple to understand
•  It is based on all observations of given data

Demerit of Arithmetic Mean

•  It can neither be determined by inspection or by graphical location.
•  It cannot be computed when class intervals have open ends.
•  If any one of the data is missing then mean cannot be calculated.

MEDIAN

Median is the middle value of the dataset in which the dataset is arranged in the ascending order or in descending order. When the dataset contains an even number of values, then the median value of the dataset can be found by taking the mean of the middle two values.

Consider the given dataset with the odd number of observations arranged in descending order – 23, 21, 18, 16, 15, 13, 12, 10, 9, 7, 6, 5, and 2

Here 12 is the middle or median number that has 6 values above it and 6 values below it.

Now, consider another example with an even number of observations that are arranged in descending order – 40, 38, 35, 33, 32, 30, 29, 27, 26, 24, 23, 22, 19, and 17

When you look at the given dataset, the two middle values obtained are 27 and 29. Now, find out the mean value for these two numbers.

i.e.,(27+29)/2 =28

Therefore, the median for the given data distribution is 28.

Merits of Median

•  Median is rigidly defined as in the case of mean
•  It can also be used for quantities
•  It can be located graphically
•  It can easy to calculate and easy to understand

Demerits of Median

 Very difficult to calculate when the number of measures are large

MODE

The mode represents the frequently occurring value in the dataset. Sometimes the dataset may contain multiple modes and in some cases, it does not contain any mode at all.

Consider the given dataset 5, 4, 2, 3, 2, 1, 5, 4, 5

Since the mode represents the most common value. Hence, the most frequently repeated value in the given dataset is 5.

Merits of Mode

•  It is readily comprehensive and easy to compute
•  Mode can be located in graph also
•  It is easy to understand

Demerits of Mode

•  It is not rigidly defined
•  It is not used for further algebraic treatment.

Mode=3Median- 2Mean

             Based on the properties of the data, the measures of central tendency are selected. If you have a symmetrical distribution of continuous data, all the three measures of central tendency hold good. But most of the times, the analyst uses the mean because it involves all the values in the distribution or dataset.

 If you have skewed distribution, the best measure of finding the central tendency is the median

 If you have the original data, then both the median and mode are the best choice of measuring the central tendency.

 If you have categorical data, the mode is the best choice to find the central tendency.

Skewness in Statistics : Skewness, in statistics, is a measure of the asymmetry in a probability distribution. It measures the deviation of the curve of the normal distribution for a given set of data. The value of skewed distribution could be positive or negative or zero. Usually, the bell curve of normal distribution has zero skewness.

If in a distribution mean median mode, then that distribution is known as symmetrical distribution.

If in a distribution mean median mode, then it is not a symmetrical distribution and it is called a skewed distribution and such a distribution could either be positively skewed or negatively skewed.

Kurtosis

Kurtosis is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. The peak is the tallest part of the distribution, and the tails are the ends of the distribution.

There are three types of kurtosis:

Mesokurtic

Leptokurtic

platykurtic

Mesokurtic: Distributions those are moderate in breadth and curves with a medium peaked height.

Leptokurtic: More values in the distribution tails and more values close to the mean (i.e. sharply peaked with heavy tails)

Platykurtic: Fewer values in the tails and fewer values close to the mean (i.e. the curve has a flat peak and has more dispersed scores with lighter tails).

Measures of Dispersion

In statistics, the dispersion measures help interpret data variability, i.e. to understand how homogenous or heterogeneous the data is. In simple words, it indicates how squeezed or scattered the variable is. However, there are two types of dispersion measures, absolute and relative.

Measures of Dispersion /measures of variability are the indices of spread or scattering of individual measures. The measures of Dispersion are;

1. Range

2. Standard Deviation

3. Quartile Deviation

4. Mean Deviation

RANGE

Range is the simplest measure of variation. It defined as difference between largest value and smallest value

Range =Highest score - lowest score

For frequency distribution;

Range =[ Exact upper limit of the upper class - Exact lower limit of the Lower class ]

This is the difference between the highest and lowest scores in a distribution taking into consideration the end scores also. Thus range will be equal to H-I.+ 1, where H is the highest and L is the lowest score. 1 is added to give scope for including both the end scores in the range. Certain people consider range to be equal to H-L only. This distinction however is not serious.

Though easy to calculate, range is not a good measure of dispersion, because it takes into consideration only the end scores. Consider the following cases of two sets of scores.

Set 1: 3. 45. 47, 49, 50, 52, 53, 85

Set 2: 30, 35, 40, 50, 55, 60, 65, 70

Range of the first set = 85- 3+1=83

Range of the second set = 70-30+1 = 41

Merit of Range

•  It is the simplest measure of variation
•  It is easily determined
•  It is easily understood

STANDARD DEVIATION

In statistics, Variance and standard deviation are related with each other since the square root of variance is considered the standard deviation for the given data set. Below are the definitions of variance and standard deviation.

What is variance?

Variance is the measure of how notably a collection of data is spread out. If all the data values are identical, then it indicates the variance is zero. All non-zero variances are considered to be positive. A little variance represents that the data points are close to the mean, and to each other, whereas if the data points are highly spread out from the mean and from one another indicates the high variance. In short, the variance is defined as the average of the squared distance from each point to the mean.

What is Standard deviation?

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set. Like the variance, if the data points are close to the mean, there is a small variation whereas the data points are highly spread out from the mean, then it has a high variance. Standard deviation calculates the extent to which the values differ from the average. Standard Deviation, the most widely used measure of dispersion, is based on all values. Therefore a change in even one value affects the value of standard deviation. It is independent of origin but not of scale. It is also useful in certain advanced statistical problems.

Variance and Standard Deviation Formula

The formulas for the variance and the standard deviation is given below:

Standard Deviation Formula : The population standard deviation formula is given as:

Here,

Σ = Population standard deviation

N = Number of observations in population

Xi = ith observation in the population

Μ = Population mean

Similarly, the sample standard deviation formula is:

Here,

S = Sample standard deviation

N = Number of observations in sample

Xi = ith observation in the sample

      x= Sample mean

Variance Formula:

For example:

N = ∑f = 55

Mean = (∑fxi)/N = 925/55 = 16.818

Variance = 1/(N – 1) [∑fxi2 – 1/N(∑fxi)2]

= 1/(55 – 1) [27575 – (1/55) (925)2]

= (1/54) [27575 – 15556.8182]

= 222.559

Standard deviation = √variance = √222.559 = 14.918

Merits of Standard deviation

•  Based on all the observations
•  Most reliable measure of variability
•  Useful for further calculation

Demerits of Standard Deviation

•  It is not easy to understand
•  It is affected by extreme values
•  Difficult to interpret and calculate

QUARTILE DEVIATION

The Quartile Deviation can be defined mathematically as half of the difference between the upper and lower quartile. Here, quartile deviation can be represented as QD; Q3 denotes the upper quartile and Q1 indicates the lower quartile.

Quartile Deviation is also known as the Semi Interquartile range.

Quartile Deviation Formula

Suppose Q1 is the lower quartile, Q2 is the median, and Q3 is the upper quartile for the given data set, then its quartile deviation can be calculated using the following formula.

QD = (Q3 – Q1)/2

Quartile Deviation for Ungrouped Data

For an ungrouped data, quartiles can be obtained using the following formulas,

Q1 = [(n+1)/4]th item

Q2 = [(n+1)/2]th item

Q3 = [3(n+1)/4]th item

Where n represents the total number of observations in the given data set.

Also, Q2 is the median of the given data set, Q1 is the median of the lower half of the data set and Q3 is the median of the upper half of the data set.

Before, estimating the quartiles, we have to arrange the given data values in ascending order. If the value of n is even, we can follow the similar procedure of finding the median.

Quartile Deviation for Grouped Data

For a grouped data, we can find the quartiles using the formula,

Quartile deviation formula

Here,

Qr = the rth quartile

L1 = the lower limit of the quartile class

L2 = the upper limit of the quartile class

F = the frequency of the quartile class

C = the cumulative frequency of the class preceding the quartile class

N = Number of observations in the given data set

Quartile Deviation Example

Let’s understand the quartile deviation of ungrouped and grouped data with the help of examples given below.

Example :

Find the quartiles and quartile deviation of the following data:

17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

Solution:

Given data:

17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

Ascending order of the given data is:

2, 5, 7, 7, 8, 8, 10, 10, 14, 15, 17, 18, 24, 27, 28, 48

Number of data values = n = 16

Q2 = Median of the given data set

n is even, median = (1/2) [(n/2)th observation and (n/2 + 1)th observation]

= (1/2)[8th observation + 9th observation]

= (10 + 14)/2

= 24/2

= 12

Q2 = 12

Now, lower half of the data is:

2, 5, 7, 7, 8, 8, 10, 10 (even number of observations)

Q1 = Median of lower half of the data

= (1/2)[4th observation + 5th observation]

= (7 + 8)/2

= 15/2

= 7.5

Also, the upper half of the data is:

14, 15, 17, 18, 24, 27, 28, 48 (even number of observations)

Q3= Median of upper half of the data

= (1/2)[4th observation + 5th observation]

= (18 + 24)/2

= 42/2

= 21

Quartile deviation = (Q3 – Q1)/2

= (21 – 7.5)/2

= 13.5/2

= 6.75

Therefore, the quartile deviation for the given data set is 6.75.

Merits of Quartile Deviation

•  It is not depend on extreme values
•  It is useful in open end classes
•  It is more representative than the range

Demerits of Quartile Deviation

•  It is focus only on the middle part
•  It is less reliable than standard deviation

MEAN DEVIATION

The mean deviation is defined as a statistical measure that is used to calculate the average deviation from the mean value of the given data set. The mean deviation of the data values can be easily calculated using the below procedure.

Step 1: Find the mean value for the given data values

Step 2: Now, subtract the mean value from each of the data values given (Note: Ignore the minus symbol)

Step 3: Now, find the mean of those values obtained in step 2.

Mean Deviation Formula

The formula to calculate the mean deviation for the given data set is given below.

Mean Deviation = [Σ |X – µ|]/N

Here,

Σ represents the addition of values

X represents each value in the data set

µ represents the mean of the data set

N represents the number of data values

| | represents the absolute value, which ignores the “-” symbol

Mean Deviation Examples

Example :

Determine the mean deviation for the data values 5, 3,7, 8, 4, 9.

Solution:

Given data values are 5, 3, 7, 8, 4, 9.

We know that the procedure to calculate the mean deviation.

First, find the mean for the given data:

Mean, µ = ( 5+3+7+8+4+9)/6

µ = 36/6

µ = 6

Therefore, the mean value is 6.

Now, subtract each mean from the data value, and ignore the minus symbol if any

(Ignore”-”)

5 – 6 = 1

3 – 6 = 3

7 – 6 = 1

8 – 6 = 2

4 – 6 = 2

9 – 6 = 3

Now, the obtained data set is 1, 3, 1, 2, 2, 3.

Finally, find the mean value for the obtained data set

Therefore, the mean deviation is

= (1+3 + 1+ 2+ 2+3) /6

= 12/6

= 2

Hence, the mean deviation for 5, 3,7, 8, 4, 9 is 2.

Merits of Mean Deviation

•  Based on the all the observations
•  Very simple measure of variability
•  Easy to understand

Demerits of Mean Deviation

•  Calculation become difficult when the number of observation is large
•  Consider only absolute values

CORRELATION

Correlation refers to a process for establishing the relationships between two variables. It is to plot them on a “scatter plot”. While there are many measures of association for variables which are measured at the ordinal or higher level of measurement, correlation is the most commonly used approach.

The correlation coefficient is usually represented using the symbol r, and it ranges from -1 to +1.

A correlation coefficient quite close to 0, but either positive or negative, implies little or no relationship between the two variables. A correlation coefficient close to plus 1 means a positive relationship between the two variables, with increases in one of the variables being associated with increases in the other variable.

A correlation coefficient close to -1 indicates a negative relationship between two variables, with an increase in one of the variables being associated with a decrease in the other variable. A correlation coefficient can be produced for ordinal, interval or ratio level variables, but has little meaning for variables which are measured on a scale which is no more than nominal.

Correlation Coefficient

The correlation coefficient, r, is a summary measure that describes the extent of the statistical relationship between two interval or ratio level variables. The correlation coefficient is scaled so that it is always between -1 and +1. When r is close to 0 this means that there is little relationship between the variables and the farther away from 0 r is, in either the positive or negative direction, the greater the relationship between the two variables.

The two variables are often given the symbols X and Y. In order to illustrate how the two variables are related, the values of X and Y are pictured by drawing the scatter diagram, graphing combinations of the two variables. The scatter diagram is given first, and then the method of determining Pearson’s r is presented. From the following examples, relatively small sample sizes are given. Later, data from larger samples are given.

Scatter Diagram

A scatter diagram is a diagram that shows the values of two variables X and Y, along with the way in which these two variables relate to each other. The values of variable X are given along the horizontal axis, with the values of the variable Y given on the vertical axis.

Later, when the regression model is used, one of the variables is defined as an independent variable, and the other is defined as a dependent variable. In regression, the independent variable X is considered to have some effect or influence on the dependent variable Y. Correlation methods are symmetric with respect to the two variables, with no indication of causation or direction of influence being part of the statistical consideration. A scatter diagram is given in the following example. The same example is later used to determine the correlation coefficient.

Types of Correlation

The scatter plot explains the correlation between the two attributes or variables. It represents how closely the two variables are connected. There can be three such situations to see the relation between the two variables –

Positive Correlation – when the values of the two variables move in the same direction so that an increase/decrease in the value of one variable is followed by an increase/decrease in the value of the other variable.

Negative Correlation – when the values of the two variables move in the opposite direction so that an increase/decrease in the value of one variable is followed by decrease/increase in the value of the other variable.

No Correlation – when there is no linear dependence or no relation between the two variables.

Pearson correlation coefficient (r)

The Pearson correlation coefficient (r) is the most common way of measuring a linear correlation. It is a number between –1 and 1 that measures the strength and direction of the relationship between two variables. The Pearson correlation coefficient (r) is the most widely used correlation coefficient and is known by many names:

 Pearson’s r

 Bivariate correlation

 Pearson product-moment correlation coefficient (PPMCC)

 The correlation coefficient

The Pearson correlation coefficient is a descriptive statistic, meaning that it summarizes the characteristics of a dataset.

Specifically, it describes the strength and direction of the linear relationship between two quantitative variables.

The Pearson correlation coefficient is also an inferential statistic, meaning that it can be used to test statistical hypotheses.

Spearman’s rank correlation

In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter (rho) or as is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function.

Applications of Statistics

Statistics have huge applications across various fields in Mathematics as well as in real life. Some of the applications of statistics are given below:

 Applied statistics, theoretical statistics and mathematical statistics

 Machine learning and data mining

 Statistics in society

 Statistical computing

 Statistics applied to the mathematics of the arts

Statistics in Education:

Measurement and evaluation are essential part of teaching learning process. In this process we obtained scores and then interpret these score in order to take decisions. Statistics enables us to study these scores objectively. It makes the teaching learning process more efficient.

The knowledge of statistics helps the teacher in the following way:

 It helps the teacher to provide the most exact type of description:

When we want to know about the pupil we administer a test or observe the child. Then from the result we describe about the pupil’s performance or trait. Statistics helps the teacher to give an accurate description of the data.

 It makes the teacher definite and exact in procedures and thinking:

Sometimes due to lack of technical knowledge the teachers become vague in describing pupil’s performance. But statistics enables him to describe the performance by using proper language, and symbols. Which make the interpretation definite and exact.

 It enables the teacher to summarize the results in a meaningful and convenient form:

Statistics gives order to the data. It helps the teacher to make the data precise and meaningful and to express it in an understandable and interpretable manner.

 

Statistics helps to draw conclusions as well as extracting conclusions. Statistical steps also help to say about how much faith should be placed in any conclusion and about how far we may extend our generalization.

 It helps the teacher to predict the future performance of the pupils:

Statistics enables the teacher to predict how much of a thing will happen under conditions we know and have measured. For example the teacher can predict the probable score of a student in the final examination from his entrance test score. But the prediction may be erroneous due to different factors. Statistical methods tell about how much margin of error to allow in making predictions.

 Statistics enables the teacher to analyse some of the causal factors underlying complex and otherwise be-wildering events:

It is a common factor that the behavioural outcome is a resultant of numerous causal factors. The reason why a particular student performs poor in a particular subject are varied and many. So with the appropriate statistical methods we can keep these extraneous variables constant and can observe the cause of failure of the pupil in a particular subject.

Concept map

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SERVICE BOOK

 Learning objectives

The learning outcome of maintaining a service book can vary depending on the context, but here are some potential benefits:

Benefits for Individuals

1. Improved record-keeping skills: Maintaining a service book helps individuals develop organizational skills and attention to detail.

2. Better time management: Regularly updating the service book can help individuals prioritize tasks and manage their time more effectively.

3. Enhanced accountability: A service book provides a clear record of work done, which can promote accountability and transparency.

Benefits for Organizations

1. Accurate tracking of work history: A service book provides a comprehensive record of work done, which can help organizations track employee performance and identify areas for improvement.

2. Improved maintenance planning: By analyzing the service book, organizations can identify patterns and trends, enabling them to plan maintenance more effectively.

3. Enhanced customer satisfaction: A well-maintained service book can help organizations demonstrate their commitment to quality and customer satisfaction.

Other Benefits

1. Knowledge retention: A service book can serve as a knowledge repository, capturing the experiences and insights of individuals and teams.

2. Quality control: Regularly reviewing the service book can help organizations identify areas for quality improvement and implement corrective actions.

3. Compliance: In some industries, maintaining a service book is a regulatory requirement. By doing so, organizations can ensure compliance and avoid potential penalties.

SERVICE BOOK

Service book is for the teacher and non-teaching Staff including Librarian. It should be opened and maintained for every employee of a government Sponsored Aided junior High / High/ H S school immediately after his / her joining in Service. It is a document to record all the events of an employee in his / her entire Service period and career, recording each and every administrative actions concerning the employee right from the stages of his recruitment till his retirement to reflect the history of service of an employee. Retirement benefits like pension and gratuity would not be delayed, if the records in the service books of Teachers / Non teaching staff are kept accurately  from the beginning to the end of their Service .

Service book is mandatory :

According to Government Memorandum 1980 EDN (S) dated 15.12.1971 it is record the mandatory to record the service details of Teacher / Non. teaching staff, working in all the recognised aided schools in their service books. 

Addition/Alteration in service book :

Entries Should be made in the service book at the end of every year and all entries in the service book should be signed / attested by the Head master, but if the employee is the HM /Teacher in charge entries signed by President of Managing Committee (MC) / Administrator. If any addition or alteration is also made and attested same as above 

Certificate of verification :

It shall be the duty of the Head master to initiate action to show the service Book to the teaches every year and to obtain their signature there in after having inspected the Service Books. 

The HM / President / Administrator, as the case may be, will record a Certificate in a service book in a year. A certificate should be entered once on completing every page of history of service portion in following manner with Signature and seal of Head of the Institution (HOI). 

New school new service book :

In case HM/Assistant Teacher (AT) /any non- teaching Staff including Librarian Serving more than one school he/she should have a seperate service book for each school he/she had served with up to date entries transferred to the school he joins for further entries.

Maintain regularly :

Most augmenting position of performance area of an Head the Institution (Hol) from his staff numbers probably depends upon regular maintaining of service Book. Confidence level of your teachers and non-teaching  staff over you goes remarkably high it you are a little bit keen to their service book affairs. More you do it, less you experience discontent from their end 

Keep Service Book Neat and Clean :

• No unnecessary, extra entry

• Put only relevant, pertinent matters point wise in precise and lucid manner 

• Keep writing neatly as much as you can.

• Avoid using white ink.

• Make a habit of pen-through following by countersigning if errors detected 

Format of Service book :

It is a very Crucial document of a employee. For each government employee a register is opened which is called service book. This service book as appears in the name has all important information of employee beginning his carrier in government including documents which a candidate submit while applying post. 

It's first page contain employee full personal details viz name, date of birth, father name, educational qualification home town, photo, Identification mark etc. It contain family details, nomination form for gratuity, GPF fund, insurance etc. 

It contain all information relating to employment viz, Initial appointment, promotion, increment, pay fixation, leave LTC records, transfer, Joining, any punishment, rewards and most important is service verification entry which is necessary to count Service for pension purpose. Copies of all promotion, pay fixation, transfer also attached In this book. 

It is very important document and it goes office to office with employee with their posting and can not be prepared again as it is very difficult to gather all information for past service records which may be more then 30 years. Now it has been decided to make two copy of the service book i.e one of the keep with employee and other with employer. 

E Service book / Digitalise service book :

In order to ensure the accuracy & precision of service records government have given approval in principle for launching e-Service Book for Gazetted and Non Gazetted employee of State Government instead of physical Service

Book using the web portal, Government employees can view his/her service Book entries on their devices. The entries once viewed are also stored offline on the device and can be viewed lates on without internet connectivity. In  case of transfer of an employee from one office to other, service book will transferred online and all data related with employee will be instantly available to new organisation. 

The roll out of e-Service Book is a vital Step towards establishing a fully automated Human Resource Management System (HRMS) with an employee portal covering all employees of Government of India so that all processes of personal management from "hiring to retiring" on digital platform dispensing the Manual system of handling personnel  management.

 

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