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- Linear Equations In Two Variables
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- Congruence Of Triangles And Inequalities In A Triangle
- Quadrilaterals
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- Mean Median And Mode Of Ungrouped Data
- Probability
RS Aggarwal Solutions Class 9 Mathematics Solutions for Mean Median And Mode Of Ungrouped Data Exercise 18D in Chapter 18 - Mean Median And Mode Of Ungrouped Data
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The numbers 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 have been arranged in an ascending order and their
median is 55. Find the value of x and hence find the mode of the given data.
We know that
Number of observations = 9
By arranging the numbers in ascending order
We get
52, 53, 54, 54, (2x + 1), 55, 55, 56, 57
So we get
Median = [(n + 1)/2]th value
By substituting the values
Median = [(9 + 1)/2]th value
We get
Median = 5th value = 2x + 1
It is given that median = 55
We can write it as
2x + 1 = 55
On further calculation
2x = 54
By division
x = 27
By substituting the value of x
2x + 1 = 2(27) + 1 = 55
So we get
52, 53, 54, 54, 55, 55, 55, 56, 57
We know that 55 occurs the maximum number of times so the mode is 55.
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