Question

If the mean of 50 scores is exactly 26,4, and the mean of 49 of those scores is exactly 26, is the 50 score ?

Answer 1

The 50th score is 46.

Explanation:

Given that

`a_(50) = 26.4\\a_(49) = 26\\n_1 = 50\\n_2 = 49`

In order to find the 50th score we have to find sum of 49 values and 50 values and then subtract them.

Average is given by the formula:

`Average = (Sum)/(Number\ of\ values)\\`

Using this formula, we can calculate sum for both averages

So,

`a_(50) = (s_(50))/(n_1)\\26.4 = (s_(50))/(50)\\26.4*50 = s_(50)\\s_(50) = 1320`

And

`a_(49) = (s_(49))/(n_2)\\26.4 = (s_(49))/(49)\\26*49 = s_(49)\\s_(49) = 1274`

Now for the 50th score,

`50th\ score = s_(50) - s_(49) = 1320-1274 = 46`

Hence,

The 50th score is 46.