R.D. Sharma Solutions Class 9th: Ch 24 Measure of Central Tendency Exercise 24.4

Given that the marks obtained by 15 students are 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 9, 8, 7 and 7.
Make the following frequency table.

Since, the value 7 occurs maximum number of times, that is, 4. Hence, the mode value is 7.

2. Find the mode from the following data:
125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125

Solution

The given data is 125, 175, 225, 125, 225, 175, 325, 125, 375, 225, and 125.
Make the following frequency table.

Since, the value 125 occurs maximum number of times, that is, 4. Hence, the mode value is 125.

3. Find the mode for the following series:
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2

Solution

The given series is 7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6 and 7.2.
Make the following frequency table.

Since, the value 7.2 occurs maximum number of times, that is, 4. Hence, the modal value is 72.

4. Find the mode of the following data in each case:
(i) 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
(ii) 7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7

Solution

(i) The given data is 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14 and 18.
Make the following frequency table.

Here,14 occurs maximum number of times (that is 4). Hence, the modal value is 14.

(ii) The given data is 7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18 and 7.
Make the following frequency table.

Since, the value 7 occurs maximum number of times, that is, 5. Hence, the modal value is 7.

5. The demand of different shirt sizes, as obtained by a survey, is given below:

Size:	38	39	40	41	42	43	44	Total
Number of persons (wearing it):	26	39	20	15	13	7	5	125

Find the modal shirt sizes, as observed from the survey.

Solution

The demand of different shirt sizes is given as:

Here, x denotes the size of the shirts and f denotes the number of peoples (frequency) wearing it.
The value 39 occur maximum number of times, that is, 39. Hence, the modal shirt size is 39.