Question

Suppose thatTis a data set with the values{3,6,7,4,6,5, x}. If the mean and median ofTareequal, what is the sum of all possible values ofx?

Answer 1

15

Explanation:

We are given that a set

T={3,6,7,4,6,5,x}

Arrange in ascending order

3,4,5,6,6,7,x

Sum of data=3+4+5+6+6+7+x=31+x

Total number of observations=7

Mean=
`(sum\;of\;observations)/(total\;number\;of\;observations)`

Mean=
`(31+x)/(7)`

n is odd therefore median=
`((n+1)/(2))^(th)=(7+1)/(2)=4^(th)`observation

If x is less than 6

Median=5

Median=Mean

`(31+x)/(7)=5`

`31+x=5(7)=35`

`x=35-31=4`

If x is greater than 5

Median=6

`(31+x)/(7)=6`

`31+x=6(7)=42`

`x=42-31=11`

The sum of possible values of x=4+11=15