Finite Math Examples

$3$ , $7$ , $13$ , $19$ , $22$ , $21$ , $17$ , $10$ , $8$ , $1$ , $8$ , $13$ , $15$ , $24$ , $17$ , $13$ , $4$ , $10$ , $15$ , $20$

Step 1

The number of classes can be estimated using the rounded output of Sturges' rule, $N = 1 + 3.322 \log (n)$ , where $N$ is the number of classes and $n$ is the number of items in the data set.

$1 + 3.322 \log (14) = 4.80743733$

Step 2

Select $5$ classes for this example.

$5$

Step 3

Find the data range by subtracting the minimum data value from the maximum data value. In this case, the data range is $24 - 1 = 23$ .

$23$

Step 4

Find the class width by dividing the data range by the desired number of groups. In this case, $\frac{23}{5} = 4.6$ .

$4.6$

Step 5

Round $4.6$ up to the nearest whole number. This will be the size of each group.

$5$

Step 6

Start with $1$ and create $5$ groups of size $5$ .

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 1 - 5 \\ 6 - 10 \\ 11 - 15 \\ 16 - 20 \\ 21 - 25 \end{array}$

Step 7

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

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 1 - 5 & 0.5 - 5.5 \\ 6 - 10 & 5.5 - 10.5 \\ 11 - 15 & 10.5 - 15.5 \\ 16 - 20 & 15.5 - 20.5 \\ 21 - 25 & 20.5 - 25.5 \end{array}$

Step 8

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

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 1 - 5 & 0.5 - 5.5 & | | | \\ 6 - 10 & 5.5 - 10.5 & | | | | | \\ 11 - 15 & 10.5 - 15.5 & | | | | | \\ 16 - 20 & 15.5 - 20.5 & | | | | \\ 21 - 25 & 20.5 - 25.5 & | | | \end{array}$

Step 9

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

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 1 - 5 & 0.5 - 5.5 & 3 \\ 6 - 10 & 5.5 - 10.5 & 5 \\ 11 - 15 & 10.5 - 15.5 & 5 \\ 16 - 20 & 15.5 - 20.5 & 4 \\ 21 - 25 & 20.5 - 25.5 & 3 \end{array}$