The mean of four positive integers is 5 . The median of the four integers is 6 . What is the mean of the largest and smallest of the integers
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Given:
The mean of four positive integers is 5 and the median of the four integers is 6
To Find:
What is the mean of the largest and smallest of the integers?
Solution:
Let us consider the 4 numbers be: A, B, C and D arranged in ascending order .
So, we get, A as the smallest and D as the largest number.
Mean = (A + B + C + D)/4
⇒ 5 = (A + B + C + D)/4
∴ A + B + C + D = 20
Median = ( B + C)/2
⇒ 6 = (B + C)/2
∴ B + C = 12
⇒ A + 12 + D = 20
⇒ A + D = 8
⇒ (A + D)/2 = 4
Therefore, the mean of the largest and smallest of the integers = 4
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