Answer:
15
Step-by-step 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=[tex]\frac{sum\;of\;observations}{total\;number\;of\;observations}[/tex]
Mean=[tex]\frac{31+x}{7}[/tex]
n is odd therefore median=[tex](\frac{n+1}{2})^{th}=\frac{7+1}{2}=4^{th}[/tex]observation
If x is less than 6
Median=5
Median=Mean
[tex]\frac{31+x}{7}=5[/tex]
[tex]31+x=5(7)=35[/tex]
[tex]x=35-31=4[/tex]
If x is greater than 5
Median=6
[tex]\frac{31+x}{7}=6[/tex]
[tex]31+x=6(7)=42[/tex]
[tex]x=42-31=11[/tex]
The sum of possible values of x=4+11=15
