Question

After six biology tests, Ruben has a mean score of 79. What score does Ruben need on the next test to raise his average (mean) to 81?

Answer 1

The means score was calculated by adding the results of the tests and dividing it by the number of tests:

`\bar{X}=(\Sigma x_i)/(n)`

→ Σxi represents the sum of the scores of the tests

→ n represents the number of tests

For the average value 79. the scores of 6 tests were added:

`79=(\Sigma x_i)/(6)`

From this expression, calculate the sum of the scores of the 6 tests:

`\begin{gathered} \Sigma x_i=79\cdot6 \\ \Sigma x_i=474 \end{gathered}`

Next, you have to calculate the score of a seventh test, so that the average score is equal to 81.

The sum of the scores of the test will be equal to the sum of the previous 6 tests plus the score of the seventh test. Let "x" represent the score on the seventh test, then Σxi=474+x will represent the sum of the scores of all tests.

This time the average has to be calculated over 7 tests, so you have to use n=7

The goal average is 81, then you can calculate the score needed as follows:

`\begin{gathered} \bar{X}=(\Sigma x_i)/(n) \\ 81=(474+x)/(7) \end{gathered}`

Multiply both sides by 7

`\begin{gathered} 81\cdot7=474+x \\ 567=474+x \end{gathered}`

Subtract 474

`\begin{gathered} 567-474=474-474+x \\ 93=x \end{gathered}`

Ruben has to score a 93 in the next test to raise his average to 81.