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Question
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is ______.
Options
28
30
35
38
Solution
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is 38.
Explanation:
Let x1, x2, x3, x4 and x5 be five numbers and one of the excluded number be x5.
Given, mean of the five numbers = 30
⇒ `(x_1 + x_2 + x_3 + x_4 + x_5)/5 = 30`
⇒ x1 + x2 + x3 + x4 + x5 = 150
⇒ x1 + x2 + x3 + x4 = 150 – x5
On dividing both sides by 4, we get
`(x_1 + x_2 + x_3 + x_4)/4 = (150 - x_5)/4` ...(i)
Given, mean of the four numbers = 28
∴ `(150 - x_5)/4 = 28` ...[From equation (i)]
⇒ 150 – x5 = 112
⇒ x5 = 150 – 112
⇒ x5 = 38
Hence, the excluded number is 38.
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