Statistics Examples

\begin{matrix} Class & Frequency 15 - 21 & 7 22 - 28 & 3 29 - 35 & 2 36 - 42 & 5 43 - 49 & 1 \end{matrix}

$\begin{array}{c} Class & Frequency \\ 15 - 21 & 7 \\ 22 - 28 & 3 \\ 29 - 35 & 2 \\ 36 - 42 & 5 \\ 43 - 49 & 1 \end{array}$

Step 1

The relative frequency of a data class is the percentage of data elements in that class. The relative frequency can be calculated using the formula

f_{i} = \frac{f}{n}

$f_{i} = \frac{f}{n}$ , where

f

$f$ is the absolute frequency and

n

$n$ is the sum of all frequencies.

f_{i} = \frac{f}{n}

$f_{i} = \frac{f}{n}$

Step 2

n

$n$ is the sum of all frequencies. In this case,

n = 7 + 3 + 2 + 5 + 1 = 18

$n = 7 + 3 + 2 + 5 + 1 = 18$ .

n = 18

$n = 18$

Step 3

The relative frequency can be calculated using the formula

f_{i} = \frac{f}{n}

$f_{i} = \frac{f}{n}$ .

\begin{matrix} Class & Frequency (f) & f_{i} 15 - 21 & 7 & \frac{7}{18} 22 - 28 & 3 & \frac{3}{18} 29 - 35 & 2 & \frac{2}{18} 36 - 42 & 5 & \frac{5}{18} 43 - 49 & 1 & \frac{1}{18} \end{matrix}

$\begin{array}{c} Class & Frequency (f) & f_{i} \\ 15 - 21 & 7 & \frac{7}{18} \\ 22 - 28 & 3 & \frac{3}{18} \\ 29 - 35 & 2 & \frac{2}{18} \\ 36 - 42 & 5 & \frac{5}{18} \\ 43 - 49 & 1 & \frac{1}{18} \end{array}$

Step 4

Simplify the relative frequency column.

\begin{matrix} Class & Frequency (f) & f_{i} 15 - 21 & 7 & 0.3 ¯ 8 22 - 28 & 3 & 0.1 ¯ 6 29 - 35 & 2 & 0. ¯ 1 36 - 42 & 5 & 0.2 ¯ 7 43 - 49 & 1 & 0.0 ¯ 5 \end{matrix}

$\begin{array}{c} Class & Frequency (f) & f_{i} \\ 15 - 21 & 7 & 0.3\overline{8} \\ 22 - 28 & 3 & 0.1\overline{6} \\ 29 - 35 & 2 & 0.\overline{1} \\ 36 - 42 & 5 & 0.2\overline{7} \\ 43 - 49 & 1 & 0.0\overline{5} \end{array}$

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