Question

The mean of a list of test scores is 80. Adding an additional test score of 92 caused the mean to rise to 82. After this additional, how many total test are in the list

Answer 1

Answer:

6

Step-by-step explanation:

The mean of a list of test scores is 80

Adding an additional test score of 92 caused the mean to rise to 82

To find:

After this additional, how many total test are in the list ?

Solution:

Let the total number of test at first = $n$

And sum of total score = $S$

As we know, mean = $\frac{sum \ of \ total \ observation}{number\ of \ total\ observation}$

                    $80= \frac{S}{n}$

Multiplying both sides by $n$

$80n=S$

Now, as adding an additional test score of 92 caused the mean to rise to 82,

$S+92=82\times(n+1)\\80n +92 = 82n+82 \ (given \ S =80n)$

$80n-82n =82-92\\-2n=-10$

By dividing both sides by minus ( - )

$2n =10$

By dividing both sides by 2

$n =5$

Thus, total number of test at first = $n$ = 5

And, after this additional score added, total number of tests are $n+1=6$