Find the median of the given data if the mean is 4.5. : 5, 7, 7, 8, x, 5, 4, 3, 1, 2
Solution:
Given, the data is 5, 7, 7, 8, x, 5, 4, 3, 1, 2
Mean of the data is 4.5
We have to find the median of the given data.
We know, mean = sum of observations / number of observations
Sum of observation = 5 + 7 + 7 + 8 + x + 5 + 4 + 3 + 1 + 2
= 42 + x
Number of observation = 10
Now, 4.5 = (42 + x)/10
42 + x = 4.5(10)
42 + x = 45
x = 45 - 42
x = 43
Now, the data is 5, 7, 7, 8, 3, 5, 4, 3, 1, 2
Arranging the data in ascending order, we get
1, 2, 3, 3, 4, 5, 5, 7, 7, 8
When the given data is arranged in ascending (or descending) order, then the middle most observation is the median of the data.
If n is even, then median = [(n/2)th term + (n/2 + 1)th term]/2
Median = [(10/2)th term + (10/2 + 1)th term]/2
= [5th term + (5+1)th term]/2
= [5th term + 6th term]/2
= (4 + 5)/2
= 9/2
= 4.5
Therefore, the median is 4.5.
✦ Try This: Find the median of the given data if the mean is 6.3. 2, 3, 3, 5, x, 8, 2, 5, 10, 12
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 3
NCERT Exemplar Class 7 Maths Chapter 3 Problem 58
Find the median of the given data if the mean is 4.5. : 5, 7, 7, 8, x, 5, 4, 3, 1, 2
Summary:
The median of the given data 5, 7, 7, 8, x, 5, 4, 3, 1, 2 if the mean is 4.5, is 4.5
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