Class 9 RD Sharma Solutions Chapter 24 Measures of Central Tendency Exercise 24.4 (original) (raw)

Last Updated : 19 Sep, 2024

Exercise 24.4 in RD Sharma's Class 9 textbook delves into the calculation and interpretation of measures of central tendency for grouped data, a crucial skill in statistics and data analysis. This exercise builds upon previous knowledge of mean, median, and mode, extending these concepts to more complex datasets where individual values are grouped into intervals or classes.

The exercise typically covers techniques such as using the direct method and assumed mean method for calculating the mean of grouped data, employing the median formula to find the middle value in a grouped dataset, and utilizing the mode formula to identify the most frequent class.

**Question 1. Find out the mode of the following marks obtained by 15 students in a class:

**Marks: 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 9, 8, 7, 7.

**Solution:

The mode is the most common number that occurs frequently in the given data.

**Marks	**4	**5	**6	**7	**8	**9	**10
**Number of students	**2	**2	**2	**4	**2	**2	**1

Here, we can see that 7 occurred most frequently.
Hence, Mode = 7

**Question 2. Find out the mode from the following data :

**125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125

**Solution:

The frequency of given set of observations:

**Values	**125	**175	**225	**325	**375
**Frequency	**4	**2	**3	**1	**1

Here the maximum frequency is 4 which is 125.
Hence, Mode = 125

**Question 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:

Frequency of the given set of observations:

**Values	**7.2	**7.3	**7.4	**7.5	**7.6	**7.7
**Frequency	**4	**2	**1	**2	**1	**2

Here the maximum frequency is 4 which is 7.2.
Hence, mode = 7.2

**Question 4. Find the mode of the following data in each case:

****(i) 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18**

**Solution:

First arrange the data in the ascending order:
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here we can clearly see that 14 occurs 4 times, hence it has the highest frequency.
So, mode = 14

****(ii) 7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7**

**Solution:

Frequency of the given set of observations:

**Values	**7	**9	**12	**13	**15	**18	**25
**Frequency	**5	**1	**3	**1	**1	**1	**1

Here the maximum frequency is 5 which is 7.
Hence, mode = 7.

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

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

**Solution:

Frequency of the given set of observations:

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

Here the maximum frequency is 39 which is 39.
Hence, mode = 39.

Summary

Exercise 24.4 equips students with essential tools for analyzing grouped data through measures of central tendency. It covers the calculation of mean using both direct and assumed mean methods, application of the median formula to find the central value in grouped datasets, and utilization of the mode formula to identify the most frequent class. The exercise emphasizes the importance of handling different types of class intervals, including equal and unequal widths, and interpreting results within the context of the data. Students learn to navigate frequency distribution tables, cumulative frequency distributions, and how to choose the appropriate measure based on data characteristics. This comprehensive approach not only enhances computational skills but also develops critical thinking in data interpretation, preparing students for more advanced statistical concepts and real-world data analysis challenges in various fields of study.