Analysis of Frequency Distributions - Class 11 Maths MCQ

This set of Class 11 Maths Chapter 15 Multiple Choice Questions & Answers (MCQs) focuses 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.

No. of workers	100
Average monthly wages	280
Variance of distribution of wages	10

a) 2800
b) 280
c) 28000
d) 2.8
View Answer

Answer: c
Explanation: 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
View Answer

Answer: d
Explanation: 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
View Answer

Answer: a
Explanation: 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
View Answer

Answer: b
Explanation: Coefficient of Variance = (Standard Deviation/Mean) × 100
⇒ Mean = 25600/4000 = 6.4.

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

	Height	Weight
Mean	170 cm	55 kg
Variance	130 cm²	25 kg²

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
View Answer

Answer: a
Explanation: 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.

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