Statistics Examples

$12$ , $23$ , $45$ , $56$ , $78$ , $89$ , $n = 4$

Step 1

Find the data range by subtracting the minimum data value from the maximum data value. In this case, the data range is $89 - 12 = 77$ .

$77$

Step 2

Find the class width by dividing the data range by the desired number of groups. In this case, $\frac{77}{4} = 19.25$ .

$19.25$

Step 3

Round $19.25$ up to the nearest whole number. This will be the size of each group.

$20$

Step 4

Start with $12$ and create $4$ groups of size $20$ .

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 12 - 31 \\ 32 - 51 \\ 52 - 71 \\ 72 - 91 \end{array}$

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.

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 12 - 31 & 11.5 - 31.5 \\ 32 - 51 & 31.5 - 51.5 \\ 52 - 71 & 51.5 - 71.5 \\ 72 - 91 & 71.5 - 91.5 \end{array}$

Step 6

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

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 12 - 31 & 11.5 - 31.5 & | | \\ 32 - 51 & 31.5 - 51.5 & | \\ 52 - 71 & 51.5 - 71.5 & | \\ 72 - 91 & 71.5 - 91.5 & | | \end{array}$

Step 7

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

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 12 - 31 & 11.5 - 31.5 & 2 \\ 32 - 51 & 31.5 - 51.5 & 1 \\ 52 - 71 & 51.5 - 71.5 & 1 \\ 72 - 91 & 71.5 - 91.5 & 2 \end{array}$