Statistics Examples

87

$87$ ,

54

$54$ ,

21

$21$ ,

32

$32$ ,

65

$65$ ,

98

$98$ ,

n = 5

$n = 5$

Step 1

Find the data range by subtracting the minimum data value from the maximum data value. In this case, the data range is

98 - 21 = 77

$98 - 21 = 77$ .

77

$77$

Step 2

Find the class width by dividing the data range by the desired number of groups. In this case,

\frac{77}{5} = 15.4

$\frac{77}{5} = 15.4$ .

15.4

$15.4$

Step 3

Round

15.4

$15.4$ up to the nearest whole number. This will be the size of each group.

16

$16$

Step 4

Start with

21

$21$ and create

5

$5$ groups of size

16

$16$ .

\begin{array}{c} Class & Class Boundaries & Frequency \\ 21 - 36 \\ 37 - 52 \\ 53 - 68 \\ 69 - 84 \\ 85 - 100 \end{array}

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 21 - 36 \\ 37 - 52 \\ 53 - 68 \\ 69 - 84 \\ 85 - 100 \end{array}$

Step 5

Determine the class boundaries by subtracting

0.5

$0.5$ from the lower class limit and by adding

0.5

$0.5$ to the upper class limit.

\begin{array}{c} Class & Class Boundaries & Frequency \\ 21 - 36 & 20.5 - 36.5 \\ 37 - 52 & 36.5 - 52.5 \\ 53 - 68 & 52.5 - 68.5 \\ 69 - 84 & 68.5 - 84.5 \\ 85 - 100 & 84.5 - 100.5 \end{array}

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 21 - 36 & 20.5 - 36.5 \\ 37 - 52 & 36.5 - 52.5 \\ 53 - 68 & 52.5 - 68.5 \\ 69 - 84 & 68.5 - 84.5 \\ 85 - 100 & 84.5 - 100.5 \end{array}$

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 \\ 21 - 36 & 20.5 - 36.5 & | | \\ 37 - 52 & 36.5 - 52.5 \\ 53 - 68 & 52.5 - 68.5 & | | \\ 69 - 84 & 68.5 - 84.5 \\ 85 - 100 & 84.5 - 100.5 & | | \end{array}

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 21 - 36 & 20.5 - 36.5 & | | \\ 37 - 52 & 36.5 - 52.5 \\ 53 - 68 & 52.5 - 68.5 & | | \\ 69 - 84 & 68.5 - 84.5 \\ 85 - 100 & 84.5 - 100.5 & | | \end{array}$

Step 7

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

\begin{array}{c} Class & Class Boundaries & Frequency \\ 21 - 36 & 20.5 - 36.5 & 2 \\ 37 - 52 & 36.5 - 52.5 & 0 \\ 53 - 68 & 52.5 - 68.5 & 2 \\ 69 - 84 & 68.5 - 84.5 & 0 \\ 85 - 100 & 84.5 - 100.5 & 2 \end{array}

$\begin{array}{c} Class & Class Boundaries & Frequency \\ 21 - 36 & 20.5 - 36.5 & 2 \\ 37 - 52 & 36.5 - 52.5 & 0 \\ 53 - 68 & 52.5 - 68.5 & 2 \\ 69 - 84 & 68.5 - 84.5 & 0 \\ 85 - 100 & 84.5 - 100.5 & 2 \end{array}$

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