Finite Math Examples

$18$ , $12$ , $21$ , $12$ , $11$ , $6$ , $12$ , $20$ , $18$ , $16$ , $16$ , $14$ , $15$ , $15$ , $12$ , $11$ , $8$ , $15$ , $10$ , $11$ , $21$ , $8$ , $20$ , $7$ , $14$ , $19$ , $14$ , $10$ , $20$ , $18$ , $15$ , $17$ , $21$ , $4$ , $11$ , $9$ , $26$ , $24$ , $16$ , $16$ , $15$ , $24$ , $13$ , $17$ , $10$ , $16$ , $12$ , $17$ , $19$ , $1$

Step 1

The class width can be found by finding the difference of the maximum data value and the minimum data value (range of data) divided by the number of classes.

$\frac{(Maximum Data Value - Minimum Data Value)}{(Number of Classes)} = \frac{(Range of Data)}{(Number of Classes)}$

Step 2

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.

$1 + 3.322 \log (20) = 5.32202164$

Step 3

Select $7$ classes for this example.

$7$

Step 4

Find the data range by subtracting the minimum data value from the maximum data value. In this case, the data range is $26 - 1 = 25$ .

$25$

Step 5

Find the class width by dividing the data range by the desired number of groups. In this case, $\frac{25}{7} = 3.\overline{571428}$ .

$3.\overline{571428}$

Step 6

Round $3.\overline{571428}$ up to the nearest whole number. This will be the size of each group.

$4$