# 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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