Question 1

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) 6

Accepted Answer

(C) 0 Hint: Var (X) = = – 100 = 0 ∴ S.D. = 0

Question 2

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 patients

Accepted Answer

(A) 5 patients

Question 3

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) 48

Accepted Answer

(B) 40

Question 4

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 ske

Accepted Answer

(D) Coefficient of variation

Question 5

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) 6

Accepted Answer

(A) 5

Question 6

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.

Accepted Answer

(C) S.D.

Question 7

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 = 3

Accepted Answer

(B) 8

Question 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 these

Accepted Answer

(B) Half of the range

Question 9

Question 9: Given the heights (in cm) of two groups of students: Group A: 131 cm, 150 cm, 147 cm, 138 cm, 144 cm Group B: 139 cm, 148 cm, 132 cm, 151 cm, 140 cm Which of the following is/are t

Accepted Answer

(C) Both I and II

Question 10

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%

Accepted Answer

(B) 16.67%

Question 11

Question 1: Find the range for the following data. 76, 57, 80, 103, 61, 63, 89, 96, 105, 72

Accepted Answer

Here, largest value (L) = 105, smallest value (S) = 57 ∴ Range = L – S = 105 – 57 = 48

Question 12

Question 2: Find the range for the following data. 116, 124, 164, 150, 149, 114, 195, 128, 138, 203, 144

Accepted Answer

Here, largest value (L) = 203, smallest value (S) = 114 ∴ Range = L – S = 203 – 114 = 89

Question 13

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

Accepted Answer

Here, largest value (L) = 40, smallest value (S) = 10 ∴ Range = L – S = 40 – 10 = 30

Question 14

Question 4: Find the range of the following data.

Accepted Answer

Here, upper limit of the highest class (L) = 175 lower limit of the lowest class (S) = 115 ∴ Range = L – S = 175 – 115 = 60

Question 15

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

Accepted Answer

Step-by-step solution provided.

Question 16

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

Accepted Answer

Step-by-step solution provided.

Question 17

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

Accepted Answer

Step-by-step solution provided.

Question 18

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

Accepted Answer

Step-by-step solution provided.

Question 19

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

Accepted Answer

Since data is not continuous, we have to make it continuous. let u = Calculation of variance of u:

Question 20

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

Accepted Answer

Since data is not continuous, we have to make it continuous. Let u = Calculation of variance of u: ∴ Var (X) = h2 var (u) = (10)2 × 1.4875 = 100 × 1.4875 = 148.75 ∴ S.D. = σx = √Var(X) = √148.75 = 12.2

Question 21

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 3

Accepted Answer

n = 20, = 20, σx = 5 …..(given) ∴ = 20 × 20 = 400 Corrected Σxi = Σxi – (incorrect observation) + (correct observation) = 400 – 30 + 13 = 383 Corrected = – (incorrect observation)2 + (correct observation)2 = 8500 – (30)2 + (13)2 = 8500 – 900 + 169 = 7769

Question 22

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.

Accepted Answer

Step-by-step solution provided.

Question 23

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. Fin

Accepted Answer

Let n1 and n2 be the number of boys and girls respectively. Let n = 200, = 65, = 70, = 62, σ1 = 8, σ2 = 10 Here, n1 + n2 = n n1 + n2 = 200 ……(i) Combined mean () = 65 = …… [From (i)] 70n1 + 62n2 = 13000 35n1 + 31n2 = 6500 …..(ii) Solving (i) and (ii), we get n1 = 75, n2 = 125 Number of boys = 75

Question 24

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.

Accepted Answer

Step-by-step solution provided.

Question 25

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

Accepted Answer

Step-by-step solution provided.

Question 26

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?

Accepted Answer

Here, C.V. of boys > C.V. of girls ∴ The Series of boys is more variable.

Question 27

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.

Accepted Answer

Here, C.V. (I) > C.V. (II) ∴ The brand I is more variable.

Question 28

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

Accepted Answer

Step-by-step solution provided.

Question 29

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

Accepted Answer

Let u = Calculation of variance of u:

Question 30

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.

Accepted Answer

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

Chapter 8 Measures of Dispersion Miscellaneous Exercise 8 Solutions