Chapter-6: Mean, Median and Standard Deviation(Research Methodology)-Note-PU

 

CHAPTER: SIX

MEAN, MEDIAN AND STANDAR DEVIATION

6.1 Definition

6.2 Analysis and Presentation of data

6.1-Definition

Mean

-Mean is defined as the arithmetic average of all observations in the data set.

-It requires measurement on all observation.

-It is affected by extreme values.

-It can be treated algebraically.

 

Calculation of mean

It can be calculated as the average of all observation data by using the formula given below.

Where,

=Sum of all observation data

n= number of observation

X̅ = mean of observed data

Median

-It is defined as the middle value in the data set arranged in ascending or descending order.

-It does not require measurement on all observation data.

-It is not affected by extreme values.

-It cannot be treated algebraically.

 

Calculation of median:

It is calculated by using different formula for different data bases.

1.) Formula for Databases with Odd number.

Median = (n+1)/2term , n = number of items in the set

2.) Formula for Databases with Even number.

  where, n = number of items in the set

Mode

-It is defined as the most frequently occurring values in the distribution, it has the largest frequency.

-It does not require measurement on all observations.

-It is not affected by extreme values.

-It cannot be treated algebraically.

 

Calculation of mode

It is calculated by using the formula given below.

Where, L = lower limit of modal class

f_m = frequency of modal class

f₁ = frequency of class preceding the modal class

f₂ = frequency of class succeeding the modal class

h = size of class interval

 Standard Deviation

-These statistics measure the average scatter around the mean – how longer values fluctuate above it and how smaller values fluctuate below it.

 

It is calculated by using formula given below.

Where, X̅ = sample mean

x_i = each number in the set

n = number of item in the sample