Mean, Mode, Median, AD, SD


uniform frequency distribution


no. of entries --->

Serial  Lower Limit Upper Limit Frequency
Mean--> Median --->
Mode--> av. deviation ---->
    sd. deviation ---->
    1st Quartile  ----> q1
    3rd Quartile ----> q3
    quartile deviation-->
    coefficient of variation
  Mean   + sd    =
  Median + sd    =
Sheppard correction σc  
    % percentile Pp

 Increment to be zero or 1. Mean =ΣfX /N  where f is frequency and X is the mid-point of scores in interval.

Median= L + ( N/2 - F)* i /fm   where L is the exact lower limit of the class interval upon which the median lies, N is total no. of scores, F is sum of scores of all

intervals  below L, fm is the frequency  within the interval  upon which the median falls & i is the length of class interval. Mode=3*median - 2*Mean; Median, q1,q3 are that point in a frequency distribution below which lie 50% , 25% and 75% of the score respectively. Using the same methods by which the median and the quartiles were found, one may compute points below which lie say 20%,38%,79% etc or any percent of the scores. These points are called percentiles and designated by Pp. So P20 means 20% of the scores lie below the point.

Coefficient of variation γ shows what % the standard deviation is of the mean. It is useful in comparing the variabilities of a group upon the same test administered under different conditions such as a group of people working with and without distraction. Or it may be used to compare two groups on the same test when the groups do not differ greatly in mean.

When the intervals are wide & cumulative frequency N is small, grouping errors are introduced because the scores in an interval are not always distributed symmetrically about the mid point and the discrepancy becomes more apparent when intervals are wide and N is small.Sheppard's correction is often used to adjust the error. It is given by   σc = √( sd2 - i2/12)  where i is the interval length and sd is standard deviation.