Statistics Examples

$77$ , $41$ , $85$ , $82$ , $96$ , $93$ , $66$ , $78$ , $94$ , $50$ , $57$ , $n = 5$

Step 1

Find the data range by subtracting the minimum data value from the maximum data value. In this case, the data range is $96 - 41 = 55$ .

$55$

Step 2

Find the class width by dividing the data range by the desired number of groups. In this case, $\frac{55}{5} = 11$ .

$11$

Step 3

Add one to $11$ to get the size of each group.

$12$

Step 4

Start with $41$ and create $5$ groups of size $12$ .

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 41 - 52 \\ 53 - 64 \\ 65 - 76 \\ 77 - 88 \\ 89 - 100 \end{array}$

Step 5

Determine the class boundaries by subtracting $0.5$ from the lower class limit and by adding $0.5$ to the upper class limit.

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 41 - 52 & 40.5 - 52.5 \\ 53 - 64 & 52.5 - 64.5 \\ 65 - 76 & 64.5 - 76.5 \\ 77 - 88 & 76.5 - 88.5 \\ 89 - 100 & 88.5 - 100.5 \end{array}$

Step 6

Draw a tally mark next to each class for each value that is contained within that class.

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 41 - 52 & 40.5 - 52.5 & | | \\ 53 - 64 & 52.5 - 64.5 & | \\ 65 - 76 & 64.5 - 76.5 & | \\ 77 - 88 & 76.5 - 88.5 & | | | | \\ 89 - 100 & 88.5 - 100.5 & | | | \end{array}$

Step 7

Count the tally marks to determine the frequency of each class.

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 41 - 52 & 40.5 - 52.5 & 2 \\ 53 - 64 & 52.5 - 64.5 & 1 \\ 65 - 76 & 64.5 - 76.5 & 1 \\ 77 - 88 & 76.5 - 88.5 & 4 \\ 89 - 100 & 88.5 - 100.5 & 3 \end{array}$