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Question
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, mean = 4.5
We know that, Mean = `"Sum of all observation"/"Total number of observations"`
⇒ 4.5 = `(5 + 7 + 7 + 8 + x + 5 + 4 + 3 + 1 + 2)/10`
⇒ 4.5 × 10 = 2
⇒ 45 – 42 = x
∴ x = 3
Now, arrange the data in ascending order
1, 2, 3, 3, 4, 5, 5, 7, 7, 8.
Here, n = 10 ....(Even)
Median = `("Value of" (n/2)"th observation" + "Value of" (n/2 + 1)"th observation")/2`
= `("Value of 5th observation" + "Value of 6th observation")/2`
= `(4 + 5)/2`
= `9/2`
= 4.5
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