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

Answer:

The 50th score is 46.

Step-by-step 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:

$Average = \frac{Sum}{Number\ of\ values}$

Using this formula, we can calculate sum for both averages

So,

$a_{50} = \frac{s_{50}}{n_1}\\26.4 = \frac{s_{50}}{50}\\26.4*50 = s_{50}\\s_{50} = 1320$

And

$a_{49} = \frac{s_{49}}{n_2}\\26.4 = \frac{s_{49}}{49}\\26*49 = s_{49}\\s_{49} = 1274$

Now for the 50th score,

$50th\ score = s_{50} - s_{49} = 1320-1274 = 46$

Hence,

The 50th score is 46.