Question

After six biology tests, Ruben has a mean score of 72. What score does Ruben need on the next test to raise his average (mean) to 74?

Answer 1

Mean score is calculated by the given formula:

`\text{Mean}=\frac{\sum^{}_{}x}{n}=\frac{The\text{ sum of all the values}}{\text{Total number of values}}`

The problem says after 6 biology test (this is the total number of values), the mean score is 72, then:

`\begin{gathered} 72=\frac{\sum ^{}_{}all\text{ values}}{6}\text{ } \\ \text{The sum of all values can be found by} \\ \sum ^{}_{}\text{all 6 values=72}*6=432 \end{gathered}`

Now, the question is what score is needed on the next test to raise the mean to 74.

The new total number of values will be 7, and to the sum of all values you need to add the new score, thus:

`\begin{gathered} 74=(432+x)/(7)\text{ to find the x multiply both sides by 7} \\ 74*7=(432+x)/(7)*7 \\ 518=432+x\text{ subtract 432 from both sides} \\ 518-432=432-432+x \\ 86=x\text{ reordering} \\ x=86 \end{gathered}`

Then, the score Ruben needs on the next value to raise his average to 74 is 86