Finite Math Examples

$\begin{array}{c} Class & Frequency \\ 12 - 14 & 4 \\ 15 - 17 & 5 \\ 19 - 21 & 9 \\ 22 - 24 & 2 \end{array}$

Step 1

The lower limit for every class is the smallest value in that class. On the other hand, the upper limit for every class is the greatest value in that class.

$\begin{array}{c} Class & Frequency (f) & Lower Limits & Upper Limits \\ 12 - 14 & 4 & 12 & 14 \\ 15 - 17 & 5 & 15 & 17 \\ 19 - 21 & 9 & 19 & 21 \\ 22 - 24 & 2 & 22 & 24 \end{array}$

Step 2

The class midpoint is the lower class limit plus the upper class limit divided by $2$ .

$\begin{array}{c} Class & Frequency (f) & Lower Limits & Upper Limits & Midpoint (M) \\ 12 - 14 & 4 & 12 & 14 & \frac{12 + 14}{2} \\ 15 - 17 & 5 & 15 & 17 & \frac{15 + 17}{2} \\ 19 - 21 & 9 & 19 & 21 & \frac{19 + 21}{2} \\ 22 - 24 & 2 & 22 & 24 & \frac{22 + 24}{2} \end{array}$

Step 3

Simplify all the midpoint column.

$\begin{array}{c} Class & Frequency (f) & Lower Limits & Upper Limits & Midpoint (M) \\ 12 - 14 & 4 & 12 & 14 & 13 \\ 15 - 17 & 5 & 15 & 17 & 16 \\ 19 - 21 & 9 & 19 & 21 & 20 \\ 22 - 24 & 2 & 22 & 24 & 23 \end{array}$

Step 4

Add the midpoints column to the original table.

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) \\ 12 - 14 & 4 & 13 \\ 15 - 17 & 5 & 16 \\ 19 - 21 & 9 & 20 \\ 22 - 24 & 2 & 23 \end{array}$