250+ TOP MCQs on Statistics – Analysis of Frequency Distributions & Answers | Class 11 Maths

Mathematics Multiple Choice Questions on “Statistics – Analysis of Frequency Distributions”.

1. An analysis of the monthly wages paid to the workers of a form is given below. Calculate the total monthly wages.

a) 2800
b) 280
c) 28000
d) 2.8
Answer: c
Clarification: Number of wage earners (n₁) = 100
Mean of monthly wages (X₁) = ₹280
Mean of monthly wages = Total monthly wage/Number of workers
⇒ 280 = total monthly wages/100
⇒ Total monthly wages = 28000.

2. If the coefficient of variation is 100 the mean of the data is 25, then find the standard deviation.
a) 5
b) 10
c) 15
d) 25
Answer: d
Clarification: Coefficient of Variance = (Standard Deviation/Mean) × 100
⇒ Standard Deviation = 25.

3. If the standard deviation of a data is 820 and mean of the data is 50, find the coefficient of variation.
a) 16.4
b) 164
c) 1640
d) 1.64
Answer: a
Clarification: Coefficient of Variance = (Standard Deviation/Mean) × 100
⇒ Coefficient of Variance = (820/50) × 100 = 16.4.

4. If standard deviation of a data is 40 and the coefficient of variation is 25600, then find the mean.
a) 64
b) 6.4
c) 640
d) 0.64
Answer: b
Clarification: Coefficient of Variance = (Standard Deviation/Mean) × 100
⇒ Mean = 25600/4000 = 6.4.

5. The following data shows the heights and weights of the students of class 9. Which of the following is correct?

a) Coefficient of variation of weights > Coefficient of variation of heights
b) Coefficient of variation of weights < Coefficient of variation of heights
c) Coefficient of variation of weights = Coefficient of variation of heights
d) Coefficient of variation of weights = ½ Coefficient of variation of heights
Answer: a
Clarification: X̄₁ = 170, X̄₂ = 55, σ₁² = 130 and σ₂² = 25.
Now, Standard Deviation = √Variance
⇒ Standard deviation of height, σ₁² = 130 ⇒ σ₁ = √130 ⇒ σ₁ = 11.40
and Standard deviation of weight, σ₂² = 130 ⇒ σ₂ = √25 ⇒ σ₂ = 5
Also, Coefficient of Variance = (Standard Deviation/Mean) × 100
⇒ Coefficient of Variation in heights = (σ₁/X̄₁) x 100 = (11.40/170) x 100 = 6.7
and Coefficient of Variation in weights = (σ₂/X̄₂) x 100 = (5/55) x 100 = 9.09.