# Mathematics Questions and Answers – Statistics – Analysis of Frequency Distributions

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This set of Mathematics 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 100 280 10

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

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

Explanation: Coefficient of Variance = (Standard Deviation/Mean) × 100
⇒ Standard Deviation = 25.
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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

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

Explanation: 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?

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

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.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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