Question

The random sample of scores on a recent test were selected and recorded below68, 71, 77, 82, 85, 88, 89, 90, 92, 93, 96, 99Calculate the mean and standard deviation for the data set. Round your answers to 3 decimal places

Answer 1

From the question, we are given the scores below

$68,71,77,82,85,88,89,90,92,93,96,99$

Consider the table below

From the Data set

the mean is

$\begin{gathered} \bar{x}=\frac{68+71+77+82+85+88+89+90+92+93+96+99}{12} \\ \bar{x}=\frac{1030}{12} \\ \bar{x}=85.833 \end{gathered}$

The mean = 85.833

The standard deviation can be calculated using

$SD=\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}}$

From the table above we have

$\begin{gathered} SD=\sqrt[]{\frac{1029.668}{12}} \\ SD=\sqrt[]{85.806} \\ SD=9.263 \end{gathered}$

Therefore

The Standard deviation is 9.263