Statistics Test

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Statistics Test - 1

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Weekly Quiz Competition

Question 1
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In a frequency distribution, if the mean and median are 21 and 22 respectively, then its mode is approximately:

A
20

B
22

C
24

D
25

Solution

Given:

In a frequency distribution, the mean and median are 21 and 22 respectively.

As we know that,
Question 2
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14 observations are 10, 11, 11, 12, 13, 14, 12, 13, 10, 12, 12, 14, 14 and 15.

What is the median of the given observations?

A
12

B
13

C
14

D
10

Solution

If we sort the numbers in Ascending order,

10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 15

Here, number of elements = 14, Even

Two Middle elements are 12,12
Question 3
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What is the arithmetic mean of the data set: 4, 5, 0, 10, 8, and 3?

A
4

B
5

C
6

D
7

Solution

The arithmetic mean of the data set: 4, 5, 0, 10, 8 and 3

Here, the total numbers are 6.
Question 4
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Find the mean, variance, and standard deviation for the following distribution:

A
14, 45.8, 6.77

B
16, 45.8, 6.77

C
14, 48.8, 6.77

D
14, 45.8, 7.89

Solution
Question 5
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If mean and mode of some data are 4 and 10 respectively, its median will be:

A
2

B
3

C
4

D
6

Solution
Question 6
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The value of the coefficient of correlation r lies between:

A
0 and 1

B
-1 and 0

C
-1 and +1

D
-0.5 and +0.5

Solution
Question 7
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Difference of mode and mean is equal to:

A
3 (Median - Mean)

B
2 (Median - Mean)

C
3 (Mean Mode)

D
2 (Mode Mean)

Solution

3Median = 2Mean + Mode

3Median - 2Mean - Mean = Mode - Mean

Difference of mode and mean = 3 (Median - Mean)

∴ The difference of mode and mean is equal to 3 (Median - Mean).
Question 8
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For a symmetrical frequency distribution we have:

A
mean > mode > median

B
mean < mode < median

C
mean = mode = median

D
mode = 1/2 (mean + median)

Solution

In the case of a frequency distribution that has a symmetrical frequency curve, the empirical relation states that mean = median = mode.

In the case of a positively skewed frequency distribution curve, mean > median > mode.

In the case of negatively skewed frequency distribution mean < median < mode. mode = 1/2 (mean + median)
Question 9
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If the median of the data 24, 25, 26, (x + 2), (x + 3), 30, 31, 34 is 27.5, then x is equal to:

A
27

B
25

C
28

D
29

Solution

As we know,

The median formula of a given set of numbers, say having 'n' odd number of observations, can be expressed as:

The median formula of a given set of numbers say having 'n' even number of observations, can be expressed as:
Question 10
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A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a digit card?

A
9/13

B
2/13

C
4/13

D
5/13

Solution

Total number of cards = 52

(Digit cards are from 2 to 10. Each suit contains 4 cards. Therefore, total number of digit cards are 36 i.e. 4 × 9)

Let ‘E’ is an event of favorable outcomes. Number of favorable outcomes = 36