Statistics

                             Statistics

 Meaning- Statistics means numerical presentation of facts. Statistics is the science of collecting, classifying or organising, interpreting numerical facts(data) from the logical analysis. 

Use of Statistics in Education

1. It helps the teacher to provide the accurate description of the child. 

2. It enables the teacher to extract general conclusions. 

3. Statistics forms the basis of scientific approach to problems of Educational Psychology.

4. It proves useful in number of fields viz. railways, Banks, Army etc.

  Collection - Data collection is a process of gathering information from all the relevant sources to find a solution of the problem. 

Sources of collecting of data :-

1. Primary data - Directly from field or experiment.

2. Secondary data -Obtained from pre saved data or review. 

   Methods of Collection of data

1. Direct personal investigation

2. Observation method

3. Interview method
4. Information through Questionnaire method and Schedules. 

Classification 

Data can be classified in to two major groups :-

1. Qualitative classification(categorical)- There is no numerical relation with one another.

2. Quantitative classification(Numerical) -There is numerical relation with one another. It may be continuous or discrete.

Tabulation 

Tabulation is a systematic & logical presentation of numeric data in rows and columns. 

Central Tendencies

The common measures of central tendency (averages) are:

1. Mean or Arithmetic mean

 2. Median(Positional average) 

 3. Mode.

There are three types of series :-

1. Individual series (without frequency) 

2. Discrete series (with frequency) 

3. Continous series (class interval) 

            Mean/Arithmatic Mean

The mean is the sum of all the values in a set, divided by the number of values. 

Formula of mean for Individual Series 

Direct method :-

Shortcut method/Assumed mean method :-

Examples -

Q. 1. Find the mean of 20, 50, 70, 10, 150, 210 ?

Solution-
        Sum of variables ∑x = 20 + 50 +70 +10 +150 + 210 = 510
             Number of variables n = 6
             Mean =  ∑x∕n  =510/6 = 85

Formula of mean for Discrete series and Continous series:-

Direct method 

Shortcut method

Merits of mean

1. It has the simplest average formula which is easily understandable and easy to compute.

2. It is so rigidly defined by mathematical formula that every one gets same result for a single problem.

3. Its calculation is based on all the observations.

4. It is least affected by sampling fluctuations.

5. The mean is a typical i.e., it balances the value on either side.

6. It is the best measure to compare two or more series (datas).

7. Mean is calculated on value and does not depend upon any position.

Demerits of mean:

1. It can not be calculated if all the values are not known.

2. The extreme values have greater affect on mean.

3. It can not be determined for the qualitative data such as love, honesty, beauty etc.

                            Median 

It is the central value of the variable in a set of observations when observations

are arranged either in ascending or in descending order. 

Formula of median for Discrete series :-

Examples -

 1. Find the median of the following numbers:

 23,46,18,32,65,15,20.

Solution:

 Let us arrange the data in ascending order: 15,18,20,23,32,46,65

 number of observations is n = 7 (odd)

Median = (7+ 1)/2th item, 4th term

Now the 4th value in the data is 23.

Median is 23.

Formula of median for Continous series:- 

Merits of median

1. It is easily understood although it is not so popular as mean.

2. It is not influenced or affected by the variation in the magnitude of the extreme items.

3. The value of the median can be graphically ascertained to ogives.

4. It is the best measure for qualitative data such as beauty, intelligence etc.

5. The median indicates the value of middle item in the distribution i.e. middle most item is

the median.

6. It can be determined even by inspection in many cases.

Demerits of Median:

1. For the calculation of median, data must be arranged.

2. Median being a positional average cannot be dependent on each and every observations.

3. It is not subject to algebraic treatment.

4. Median is more affected or influenced by sampling fluctuations than the arithmetic mean.

                          Mode

Mode is the number that appears most frequently in a data.It is the most commonly observed value in a set of data. 

Note - We don't have to arrange the data in ascending/descending order during mode. 

Examples :-

1. Find the mode of the following data.

      15, 22, 17, 19, 22, 17, 29, 24, 17, 15

Ans.         Mode= 17

Formula of mode for Discrete series:-

Merits of Mode :-

1. It can be obtained by inspection.

2. It is not affected by extreme values.

3. This average can be calculated from open end classes.

4. It can be easily understood.

5. It can be used to describe qualitative phenomenon.

6. The value of mode can also be found graphically.

Demerits of Mode :-

1. Mode has no significance unless a large number of observation is available.

2. It can not be treated algebraically.

3. It is a peculiar measure of central tendency.

4. For the calculation of mode, the data must be arranged in the form of frequency distribution.

5. It is not rigidly defined measure.