## MP Board Class 9th Maths Solutions Chapter 14 Statistics Ex 14.4

Question 1.

The following number of goals were scored by a team in a series of 10 matches:

2, 3, 4, 5, 0, 1, 3, 3, 4, 3

Find the mean, median and mode of these scores.

Solution:

1.

2. Arranging the data in ascending order, we get

0, 1, 2, 3, 3, 3, 3, 4, 4, 5

n = 10 (even)

3. As 3 is repeated maximum number of times i. e., 4 times.

∴ Mode = 3

Question 2.

In a mathematics test given to 15 students, the following marks (out of 100) are recorded:

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60

Find the mean, median and mode of this data.

Solution:

1. Mean

2. Arranging the data in ascending order, we get

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

n = 15 (odd)

Median = (\(\frac{n+1}{2}\))th obseravation

= (\(\frac{15+1}{2}\))th observation = 8th obseravation

= 52.

3. As 52 is repeated maximum number of times i.e., 3 times

∴ Mode = 52

Question 3.

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.

29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Solution:

Median = 63 (given)

n = 10 (even)

2 x 63 = 2x + 2

⇒ 126 = 2x + 2

⇒ 126 – 2 = 2x

⇒ 7x = 124

x = 62

Question 4.

Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Solution:

As 14 repeated maximum number of times, mode =14.

Question 5.

Find the mean salary of 60 workers of a factory from the following table:

Solution:

Question 6.

Give one example of a situation in which

- The mean is an appropriate measure of central tendency.
- The mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Solution:

1. Mean is a quantitative central tendency of a data.

Example:

For measuring central tendency of marks of a test we find the mean of the data.

2. Median is a qualitative central tendency of a data.

Example:

For measuring central tendency of beauty of a group of women, we determine the median of the data.