Class 9 NCERT Solutions- Chapter 14 Statistics – Exercise 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:

Mean = Sum of all the elements/total number of elements

Mean = (2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3) / 10

Mean = 2.8

Now calculating Median:

Arranging the given data in ascending order, we get,

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

Median = (3 + 3) / 2 = 3

For mode, we will count the element occurring the maximum number of times.

Hence, the mode is 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:

Mean = Sum of all the elements/total number of elements.

Mean = (41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 50 + 60) / 15

Mean = 54.8

Now we have to find the median:

Arranging the given data in ascending order, we get,

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

Here the number of elements is n = 15

Thus, the middle element is the median = 52

Mode = Element 52 occurs 3 times, which is the maximum number of times.

Hence, 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:

Here, the data is already in ascending order.

Since n = 10 (an even number)

∴ Median is the average of the middlemost two elements.

Since median = 63 as given in the question

∴ (x + x + 2) / 2 = 63 

∴ x = 63 – 1 = 62

Hence, the value x is 62.

Question 4. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Solution:

When we arrange the data in ascending order, we get,

14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28.

Since data 14 is occurring the maximum number of times.

Hence, the required mode of the given data = 14

Question 5. Find the mean salary of 60 workers of a factory from the following table:

Salary (in ₹)	Number of workers
3000	16
4000	12
5000	10
6000	8
7000	6
8000	4
9000	3
10000	1
Total	60

Solution:

Calculation table based on the given data:

Salary (in Rs.)(xi)	No. of workers(fi)	fixi
3000	16	3000 * 16 = 480000
4000	12	4000 * 12 = 48000
5000	10	5000 * 10 = 50000
6000	8	6000 * 8 = 48000
7000	6	7000 * 6 = 42000
8000	4	8000 * 4 = 32000
9000	3	9000 * 3 = 27000
10000	1	10000 * 1 = 10000
Total	60	305000

Mean = (305000)/60 = 5083.33.

Thus, the required mean salary = ₹ 5083.33

Question 6. Give one example of a situation in which

(i) The mean is an appropriate measure of central tendency.

(ii) The mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Solution:

(i) Mean height of family members where all are of approximately the same height. The entries in this case will be close to each other. Therefore, the mean will be calculated as an appropriate measure of central tendency.

(ii) Median weight of a pen, a book, a Cotton Pack, a matchbox, and a Table.