If mean of the numbers $2, (2p+2), 7, 13, 17, 4$ and $(p-1)$ is 8, then find their median.

7

We're given that the mean of these numbers is 8, which means:

\(\frac{(2 + 2p + 2 + 7 + 13 + 17 + 4 + p - 1) }{7}\) = 8

4p + 46 = 56

4p = 10

p = 2.5

So, all numbers are,

(2 , 2 × 2.5 , 2 , 7 , 13 , 17 , 4 , 2.5 - 1)

= (2 , 5 , 2 , 7 , 13 , 17 , 4 , 1.5) 

Now, arrange these numbers in ascending order:

1.5 , 2 , 4, 7, 7, 13, 17

 In this case, there are 7 numbers   ( odd number )

So, Median = [\(\frac{( n + 1 )}{2}\)]th term

= [\(\frac{( 7 + 1 )}{2}\)]th term 

= 4th term

So, the median of the given numbers is 7.