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=(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=(85+88)/(2) \\ Me=(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[]{(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`