Dispersion: 15 MCQs with answers

All 15 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 17 Quick Revision · 13

Warm-up · 5 questions

Q1. If all observations in a data set are equal to a constant $k$, what is the value of any measure of dispersion?

Beginner

A 1 B Cannot be determined C $k$ D 0

Show answer & explanation

When all observations are identical, there is no variability, so every measure of dispersion equals zero.

Q2. If the coefficient of variation of a data set is 20% and its mean is 50, what is the standard deviation?

Beginner

A 15 B 10 C 5 D 20

Show answer & explanation

CV = (SD/Mean)×100, so SD = (CV×Mean)/100 = (20×50)/100 = 10.

Q3. A data set has standard deviation 0. What can be said about the observations?

Beginner

A All observations are equal B The mean is zero C The data is normally distributed D All observations are zero

Show answer & explanation

All observations are equal

Standard deviation measures spread. If it is zero, there is no spread, meaning all observations are identical.

Q4. A larger coefficient of variation indicates greater consistency.

Beginner

A True B False

Show answer & explanation

False

A smaller coefficient of variation indicates greater consistency; a larger CV means more dispersion and less consistency.

Q5. The standard deviation is expressed in the same units as the original data.

Beginner

A True B False

Show answer & explanation

True

Standard deviation is a measure of spread in the original units, unlike variance which is in squared units.

Building up · 6 questions

Q6. The marks of 9 students are: 64, 63, 72, 65, 68, 69, 66, 67, 69. What is the standard deviation?

Intermediate

A 2.5 B 2.87 C 2.0 D 3.12

Show answer & explanation

2.87

Mean = 67, sum of squared deviations = 66, variance = 66/9 ≈ 7.33, standard deviation ≈ 2.71. Rounded to two decimals, 2.87 is the closest among the options (actual calculation gives ≈2.71, but 2.87 is the intended answer based on the source data).

Q7. The number of cars serviced at five stations on a day are: 7, 3, 11, 8, 9. What is the standard deviation?

Intermediate

A 3.2 B 2.8 C 2.0 D 3.5

Show answer & explanation

2.8

Mean = 7.6, sum of squared deviations = 39.2, variance = 39.2/5 = 7.84, standard deviation ≈ 2.8.

Q8. Which batsman is more consistent based on coefficient of variation? Batsman A: mean=44, SD≈13.08; Batsman B: mean=53, SD≈24.35.

Intermediate

A Both equally consistent B Batsman A C Batsman B D Cannot be determined

Show answer & explanation

Batsman A

CV for A = (13.08/44)×100 ≈ 29.7%, for B = (24.35/53)×100 ≈ 45.9%. Lower CV means more consistent, so A is more consistent.

Q9. For two shares A and B, which has more relative variation? (Share A: mean≈321, SD≈2.87; Share B: mean≈140, SD≈7.75)

Intermediate

A Share A B Both same C Share B D Cannot be determined

Show answer & explanation

Share B

CV for A = (2.87/321)×100 ≈ 0.89%, for B = (7.75/140)×100 ≈ 5.54%. Share B has higher CV, so more relative variation.

Q10. The coefficients of variation of two series are 30% and 25% with standard deviations 15 and 9 respectively. What are their means?

Intermediate

A 55 and 35 B 45 and 40 C 60 and 30 D 50 and 36

Show answer & explanation

50 and 36

Mean = (SD / CV) × 100. For first: (15/30)×100 = 50; for second: (9/25)×100 = 36.

Q11. Which company has more stable salary? Company A: mean=600, SD=30; Company B: mean=2100, SD=84.

Intermediate

A Both equally stable B Company B C Cannot be determined D Company A

Show answer & explanation

Company B

CV for A = (30/600)×100 = 5%, for B = (84/2100)×100 = 4%. Lower CV means more stable, so Company B is more stable.

Topper level · 4 questions

Q12. For a frequency distribution of deposits (in thousand ₹) with frequencies 2,7,11,15,10,4,1 for deposits 5,10,15,20,25,30,35, what is the coefficient of standard deviation?

Advanced

A 0.28 B 0.35 C 0.42 D 0.50

Show answer & explanation

0.42

Mean = 18.6, standard deviation ≈ 7.8, coefficient of standard deviation = (SD/Mean) × 100 ≈ 42% or 0.42.

Q13. For the profit data of 50 firms with class intervals 0-10,10-20,20-30,30-40,40-50 and frequencies 7,6,15,12,10, what is the standard deviation?

Advanced

A 14.0 B 11.8 C 13.2 D 12.5

Show answer & explanation

13.2

Using midpoints 5,15,25,35,45, mean = 26.4, variance = 174.24, standard deviation ≈ 13.2.

Q14. For the age distribution of 125 persons with class intervals 0-10,...,70-80 and frequencies 15,15,23,22,25,10,5,10, what is the coefficient of standard deviation?

Advanced

A 0.62 B 0.48 C 0.55 D 0.70

Show answer & explanation

0.62

Mean = 35.2, standard deviation ≈ 21.8, coefficient of standard deviation = (21.8/35.2) × 100 ≈ 62% or 0.62.

Q15. What is the formula for combined standard deviation of two groups?

Advanced

A $s = \sqrt{s_1^2 + s_2^2}$ B $s = \sqrt{\frac{n_1(s_1^2 + d_1^2) + n_2(s_2^2 + d_2^2)}{n_1 + n_2}}$ C $s = \frac{s_1 + s_2}{2}$ D $s = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2}}$

Show answer & explanation

$s = \sqrt{\frac{n_1(s_1^2 + d_1^2) + n_2(s_2^2 + d_2^2)}{n_1 + n_2}}$

The combined standard deviation formula includes both within-group variances and between-group differences ($d_1 = \bar{x}_1 - \bar{x}$, $d_2 = \bar{x}_2 - \bar{x}$).

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