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 |
---|---|

Average monthly wages | 280 |

Variance of distribution of wages | 10 |

a) 2800

b) 280

c) 28000

d) 2.8

View Answer

Explanation: Number of wage earners (n

_{1}) = 100

Mean of monthly wages (X

_{1}) = ₹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

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

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

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 cm^{2} |
25 kg^{2} |

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

Explanation: X̄

_{1}= 170, X̄

_{2}= 55, σ

_{1}

^{2}= 130 and σ

_{2}

^{2}= 25.

Now, Standard Deviation = √Variance

⇒ Standard deviation of height, σ

_{1}

^{2}= 130 ⇒ σ

_{1}= √130 ⇒ σ

_{1}= 11.40

and Standard deviation of weight, σ

_{2}

^{2}= 130 ⇒ σ

_{2}= √25 ⇒ σ

_{2}= 5

Also, Coefficient of Variance = (Standard Deviation/Mean) × 100

⇒ Coefficient of Variation in heights = (σ

_{1}/X̄

_{1}) x 100 = (11.40/170) x 100 = 6.7

and Coefficient of Variation in weights = (σ

_{2}/X̄

_{2}) x 100 = (5/55) x 100 = 9.09.

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