# The Following are the scores of 20 students who took

The Following are the scores of 20 students who took a calculus exam. Find the mean and standard deviation of the given data. Round to the nearest tenth, if necessary.
$\begin{array}{|ccccccc|}\hline Score& 76& 82& 85& 90& 92& 95\\ Frequency& 5& 2& 3& 4& 3& 3\\ \hline\end{array}$
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Fachur
Step 1
Mean
$=\frac{\sum {x}_{i}{f}_{i}}{\sum {f}_{i}}$
$=\frac{76\left(5\right)+82\left(2\right)+85\left(3\right)+90\left(4\right)+92\left(3\right)+95\left(3\right)}{20}$
$=86$
Step 2
For standard deviation, we make a table
$\begin{array}{|ccccc|}\hline data& data-mean& \left(data-mean{\right)}^{2}& frequency& \left(data-mean{\right)}^{2}frequency\\ 76& -10& 100& 5& 500\\ 82& -4& 16& 2& 32\\ 85& -1& 1& 3& 3\\ 90& 4& 16& 4& 64\\ 92& 6& 36& 3& 108\\ 95& 9& 81& 3& 243\\ \hline\end{array}$
Then we add the values form the last column
$\sum {\left({x}_{i}-\stackrel{―}{x}\right)}^{2}{f}_{i}=950$
Then we use it to find the standard deviation
$\sqrt{\frac{\sum {\left({x}_{i}-\stackrel{―}{X}\right)}^{2}{f}_{i}}{n}}=\sqrt{\frac{950}{20}}=6.9$
Answer: $Mean=86$
Standard deviatiion $=6.9$