Question

Let us use the following dataset of exam scores{82,95,51,88,79,85,92,95,96,84}calculate the mean, median,mode,standard deviation, and variance.

Answer 1

The mean is given by:

$\begin{gathered} \mu=\frac{82+95+51+88+79+85+92+95+96+84}{10} \\ \mu=84.7 \end{gathered}$

The median is the middle value in a list of values, since it is an even number of values we have to average the middle two values, so:

$\begin{gathered} Me=\frac{85+88}{2} \\ Me=\frac{173}{2} \\ Me=86.5 \end{gathered}$

The mode is the number which appears most often in the list:

$Mo=95$

The standard deviation and the variance are given by:

$\begin{gathered} s=\sqrt[]{\frac{1}{N-1}\sum ^n_{i\mathop=1}(xi-\mu)^2} \\ so\colon \\ s\approx13.25 \end{gathered}$

And the variance is:

$s^2=175.56$