RD Sharma Solutions for Class 9 Chapter 24 Measure of Central Tendency Exercise VSAQs are provided here. This exercise helps students to revise the concepts learnt in this chapter. We, at BYJU’S, provide RD Sharma Solutions for Class 9 Maths to assist students in comprehending all the concepts. Click on the links below to access all the solutions.
RD Sharma Solutions for Class 9 Maths Chapter 24 Measure of Central Tendency Exercise VSAQs
Access Answers to RD Sharma Solutions for Class 9 Maths Chapter 24 Measure of Central Tendency Exercise VSAQs Page Number 24.21
Question 1: If the ratio of the mean and median of a certain data is 2:3, then find the ratio of its mode and mean.
Solution:
Empirical formula: Mode = 3 median – 2 mean
Since the ratio of mean and median of a certain data is 2:3, mean = 2x and median = 3x
Mode = 3(3x) – 2(2x)
= 9x – 4x
= 5x
Therefore,
Mode: Mean = 5x:2x or 5: 2
Question 2: If the ratio of mode and median of a certain data is 6:5, then find the ratio of its mean and median.
Solution: We know, Empirical formula: Mode = 3 Median – 2 Mean
Since the ratio of mode and median of a certain data is 6:5.
⇒ Mode/Median = 6/5
or Mode = (6 Median)/5
Now,
(6 Median)/5 = 3 Median – 2 Mean
(6 Median)/5 – 3 Median = – 2 Mean
or 9/10 (Median) = Mean
or Mean/ Median = 9/10 or 9:10.
Question 3: If the mean of x+2, 2x+3, 3x+4, 4x+5 is x+2, find x.
Solution:
Given: Mean of x+2, 2x+3, 3x+4, 4x+5 is x+2
We know, Mean = (Sum of all the observations) / (Total number of observations)
Sum of all the observations = x+2 + 2x+3 + 3x+4 + 4x+5 = 10x + 14
Total number of observations = 4
⇒ Mean = (10x + 14)/4
or (x + 2) = (10x + 14)/4 (using given)
4x + 8 = 10x + 14
x = -1
Question 4: The arithmetic mean and mode of the data are 24 and 12, respectively, find the median of the data.
Solution:
Given: The arithmetic mean and mode of the data are 24 and 12, respectively
We know, Empirical formula: Mode = 3 Median – 2 Mean
or 3 Median = Mode + 2 Mean
Using given values, we get
3 Median = 12 + 2(24) = 60
or Median = 20
Question 5: If the difference of the mode and median of a data is 24, then find the difference of the median and mean.
Solution:
Given: the difference of the mode and median of data is 24.
That is, Mode – Median = 24
or Mode = 24 + Median …(1)
We know, Empirical formula: Mode = 3 Median – 2 Mean
24 + Median = 3 Median – 2 Mean
(Using (1))
24 = 2 Median – 2 Mean
or 12 = Median – Mean
Therefore, the difference of the median and mean is 12.
RD Sharma Solutions for Class 9 Maths Chapter 24 Measures of Central Tendency Exercise VSAQs
Class 9 Maths Chapter 24 Measure of Central Tendency Exercise VSAQs are based on the topics, mean, median and mode of data. This exercise covers all the basic concepts helpful to solve various statistics problems. Learning the basics is certainly necessary, and the best method to study efficiently is by learning from RD Sharma Solutions, which are explained and solved chapter-wise.
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