**Chapter 8 Measures of Dispersion Miscellaneous Exercise 8**

## Chapter 8 Measures of Dispersion Miscellaneous Exercise 8

**(I) Select the correct option from the given alternatives:**

**Question 1.If there are 10 values each equal to 10, then S.D. of these values is _________(A) 100(B) 20(C) 0(D) 6Answer:**

(C) 0

Hint:

= 0

∴ S.D. = 0

**Question 2.The number of patients who visited cardiologists are 13, 17, 11, 15 in four days, then variance (approximately) is(A) 5 patients(B) 4 patients(C) 10 patients(D) 15 patientsAnswer:**

(A) 5 patients

**Question 3.If the observations of a variable X are, -4, -20, -30, -44 and -36, then the value of the range will be:(A) -48(B) 40(C) -40(D) 48Answer:**
(B) 40

**Question 4.The standard deviation of a distribution divided by the mean of the distribution and expressed in percentage is called:(A) Coefficient of Standard deviation(B) Coefficient of skewness(C) Coefficient of quartile deviation(D) Coefficient of variationAnswer:**

(D) Coefficient of variation

**Question 5.If the S.D. of first n natural numbers is √2, then the value of n must be(A) 5(B) 4(C) 7(D) 6Answer:**

(A) 5

**Question 6.The positive square root of the mean of the squares of the deviations of observations from their mean is called:(A) Variance(B) Range(C) S.D.(D) C.V.Answer:**
(C) S.D.

**Question 7.The variance of 19, 21, 23, 25 and 27 is 8. The variance of 14, 16, 18, 20 and 22 is:(A) Greater than 8(B) 8(C) Less than 8(D) 8 – 5 = 3Answer:**

(B) 8

**Question 8.For any two numbers, SD is always(A) Twice the range(B) Half of the range(C) Square of the range(D) None of theseAnswer:**

(B) Half of the range

**Question 9.Given the heights (in cm) of two groups of students:Group A: 131 cm, 150 cm, 147 cm, 138 cm, 144 cmGroup B: 139 cm, 148 cm, 132 cm, 151 cm, 140 cmWhich of the following is/are true?I. The ranges of the heights of the two groups of students are the same.II. The means of the heights of the two groups of students are the same.(A) I only(B) II only(C) Both I and II(D) NoneAnswer:**

(C) Both I and II

**Question 10.The standard deviation of data is 12 and mean is 72, then the coefficient of variation is(A) 13.67%(B) 16.67%(C) 14.67%(D) 15.67%Answer:**

(B) 16.67%

**(II) Answer the following:**

**Question 1.Find the range for the following data.76, 57, 80, 103, 61, 63, 89, 96, 105, 72Solution:**
Here, largest value (L) = 105, smallest value (S) = 57

∴ Range = L – S

= 105 – 57

= 48

**Question 2.Find the range for the following data.116, 124, 164, 150, 149, 114, 195, 128, 138, 203, 144Solution:**
Here, largest value (L) = 203, smallest value (S) = 114

∴ Range = L – S

= 203 – 114

= 89

**Question 3.Given below is the frequency distribution of weekly wages of 400 workers. Find the range.Solution:**

Here, largest value (L) = 40, smallest value (S) = 10

∴ Range = L – S

= 40 – 10

= 30

**Question 4.Find the range of the following data.Solution:**

Here, upper limit of the highest class (L) = 175

lower limit of the lowest class (S) = 115

∴ Range = L – S

= 175 – 115

= 60

**Question 5.Find variance and S.D. for the following set of numbers.25, 21, 23, 29, 27, 22, 28, 23, 21, 25Solution:**

**Question 6.Find variance and S.D. for the following set of numbers.125, 130, 150, 165, 190, 195, 210, 230, 245, 260Solution:**

**Question 7.Following data gives no. of goals scored by a team in 90 matches. Compute the standard deviation.Solution:**

**Question 8.Compute the variance and S.D. for the following data:Solution:**

**Question 9.Calculate S.D. from the following data.Solution:**

Since data is not continuous, we have to make it continuous.

let u = x−Ah=x−54.510

Calculation of variance of u:

**Question 10.Given below is the frequency distribution of marks obtained by 100 students. Compute arithmetic mean and S.D.Solution:**

Since data is not continuous, we have to make it continuous.

Calculation of variance of u:

∴ Var (X) = var (u)

= (10 × 1.4875

= 100 × 1.4875

= 148.75

∴ S.D. = = √Var(X)

= √148.75

= 12.2

**Question 11.The arithmetic mean and standard deviation of a series of 20 items were calculated by a student as 20 cm and 5 cm respectively. But while calculating them, item 13 was misread as 30. Find the corrected mean and standard deviation.Solution:**

**Question 12.The mean and S.D. of a group of 50 observations are 40 and 5 respectively. If two more observations 60 and 72 are added to the set, find the mean and S.D. of 52 items.Solution:**

**Question 13.The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. Find the number of boys and combined S.D.Solution:**

**Question 14.From the following data available for 5 pairs of observations of two variables x and y, obtain combined S.D. for all 10 observations.Solution:**

**Question 15.Calculate the coefficient of variation of the following data.23, 27, 25, 28, 21, 14, 16, 12, 18, 16Solution:**

**Question 16.The following data relates to the distribution of weights of 100 boys and 80 girls in a school.Which of the two is more variable?Solution:**
Here, C.V. of boys > C.V. of girls

∴ The Series of boys is more variable.

**Question 17.The mean and standard deviations of the two brands of watches are given below:Calculate the coefficient of variation of the two brands and interpret the results.Solution:**

Here, C.V. (I) > C.V. (II)

∴ The brand I is more variable.

**Question 18.Calculate the coefficient of variation for the data given below:Solution:**

**Question 19.Calculate the coefficient of variation for the data given below:Solution:**

Calculation of variance of u:

**Question 20.Compute the coefficient of variations for the following data to show whether the variation is greater in the field or in the area of the field.Solution:**

∴ the variation is greater in the area of the field.

**Question 21.There are two companies U and V which manufacture cars. A sample of 40 cars each from these companies is taken and the average running life (in years) is recorded.Which company shows greater consistency?Solution:**

Let denote no. of cars of company U and denote no. of cars of company V.

Here, C.V. (U) < C.V. (V)

∴ Company U shows greater consistency in performance.

**Question 22.The means and S.D. of weights and heights of 100 students of a school are as follows.Which shows more variability, weights, or heights?Solution:**

Here, C.V. for weight < C.V. for height

∴ Height shows more variability.