Question 1: Two plants A and B of a factory show following results about the number of workers and the wages paid to them.

In which plant A or B is there greater variability in individual wages?

Answer:

Variance of distribution of wages in plants:

Standard deviation of the distribution of wages in plants

We observe that the average monthly wages in both the firms is same i.e. Rs. 2500. Therefore the firm with greater variance will have more variability. Thus, firm B has greater variability in individual wages.

Question 2: The means and standard deviations of heights and weights of 50 students of a class are as follows:

Which shows more variability, heights or weight?

Answer:

Thus, Height has a greater variability than weights.

Question 3: Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?

Answer:

Question 4: Calculate coefficient of variation from the following data:

Answer:

*Calculation of Mean, Variance and Standard Deviation*

Question 5: An analysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results:

(i) Which firm A or B pays out larger amount as weekly wages?

(ii) Which firm A or B has greater variability in individual wages?

Answer:

(i)

Therefore firm B pays out larger amount as weekly wages.

(ii)

In order to compare the variability of wages among the two firms, we have to calculate their coefficients of variation.

Let and denote the standard deviations of height and weight respectively.

Further let and be the mean wages in firms A and B respectively.

Clearly, the coefficient of variation in wages is greater for firm B than for firm A. Hence, firm B shows more variability in wages.

Question 6: The following are some particulars of the distribution of weights of boys and girls in a class:

Which of the distributions is more variable?

Answer:

In order to compare the variability of weight in boys and girls, we have to calculate their coefficients of variation.

Let and denote the standard deviations of boys and girls respectively.

Further let and be the mean wages in firms A and B respectively.

Clearly, the coefficient of variation in weights is greater for boys than for girls. Hence, boys shows more variability in weights.

Question 7: The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, physics and chemistry are given below:

Which of the three subjects shows the highest variability in marks and which shows the lowest?

Answer:

In order to compare the variability of marks in mathematics, physics and chemistry, we have to calculate their coefficients of variation.

Let , and denote the standard deviations of mathematics, physics and chemistry respectively.

Further let , and be the mean marks in mathematics, physics and chemistry respectively.

Clearly, the coefficient of variation in marks is greatest in Chemistry and lowest in mathematics.

Hence, marks in chemistry show highest variability and marks in mathematics show lowest variability.

Question 8: From the data given below state which group is more variable or ?

Answer:

*Calculation of Mean, Variance and Standard Deviation*

*Calculation of Mean, Variance and Standard Deviation*

Therefore we see that Coefficient of Variation for Group 2 is more than Group 1. Hence the Group 2 is more variable.

Question 9: Find the coefficient of variation for the following data:

Answer:

*Calculation of Mean, Variance and Standard Deviation*

Question 10: From the prices of shares X and Y given below: find out which is more stable in value:

Answer:

Let the assumed mean A be 53.

Let the assumed mean A be 105.

Coefficient of variation of Y is lesser than that of X, hence price of Y is stable.

Question 11: Life of bulbs produced by two factories A and B are given below:

The bulbs of which factory are more consistent from the point of view of length of life?

Answer:

Let assumed mean A = 800 and h = 100

*Calculation of Mean, Variance and Standard Deviation*

Let assumed mean A = 800 and h = 100

*Calculation of Mean, Variance and Standard Deviation*

Since, the coefficient of variation of factor B is greater than the coefficient of variation of factory A, therefore factory B has more variability than factory A.

This means that the bulbs from factory A are more consistent from the point of views of length of life.

Question 12: Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests :

Who is more intelligent and who is more consistent?

Answer:

Let the assumed mean A be 45.

Let the assumed mean A be 55.

Since the coefficient of variation in mark obtained by Hashina is greater than the coefficient of variation in mark obtained by Ravi, so Hashina is more consistent and intelligent.