Answer :
The means score was calculated by adding the results of the tests and dividing it by the number of tests:
[tex]\bar{X}=\frac{\Sigma x_i}{n}[/tex]→ 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:
[tex]79=\frac{\Sigma x_i}{6}[/tex]From this expression, calculate the sum of the scores of the 6 tests:
[tex]\begin{gathered} \Sigma x_i=79\cdot6 \\ \Sigma x_i=474 \end{gathered}[/tex]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:
[tex]\begin{gathered} \bar{X}=\frac{\Sigma x_i}{n} \\ 81=\frac{474+x}{7} \end{gathered}[/tex]Multiply both sides by 7
[tex]\begin{gathered} 81\cdot7=474+x \\ 567=474+x \end{gathered}[/tex]Subtract 474
[tex]\begin{gathered} 567-474=474-474+x \\ 93=x \end{gathered}[/tex]Ruben has to score a 93 in the next test to raise his average to 81.
