(a) Suppose the valuable X takes the integral values from 1 to 10.

(i) Calculate the arithmetic mean.

(ii) The Standard Deviation.

(iii) The mean deviation about the arithmetic mean.

(iv) The mean deviation about the median of the value X.

(b) Also calculate the coefficient of the values of X using.

(i) Standard deviation, (ii) Mean deviation

Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree?

In a town 25% of the persons earned more than Rs. 45000, whereas 75% earned more than Rs. 18000. Calculate the absolute and relative values of dispersion.

A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their five previous scores which are:

Which batsman should be selected if we want

(i) a higher run getter, or

(ii) a more reliable batsman in the team?

To check the quality of two brands of lightbulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.

(i) Which brand gives higher life?

Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?

In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.

If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

Calculate the mean deviation about mean and standard deviation for the following distribution:

A measure of dispersion is a good .supplement to the central value in understanding a frequency distribution. Comment