Statistics Examples

$\begin{array}{c} Class & Frequency \\ 2 - 10 & 1 \\ 11 - 19 & 3 \\ 20 - 28 & 9 \end{array}$

Step 1

Find the midpoint $M$ for each class.

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) \\ 2 - 10 & 1 & 6 \\ 11 - 19 & 3 & 15 \\ 20 - 28 & 9 & 24 \end{array}$

Step 2

Multiply the frequency of each class by the class midpoint.

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) & f \cdot M \\ 2 - 10 & 1 & 6 & 1 \cdot 6 \\ 11 - 19 & 3 & 15 & 3 \cdot 15 \\ 20 - 28 & 9 & 24 & 9 \cdot 24 \end{array}$

Step 3

Simplify the $f \cdot M$ column.

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) & f \cdot M \\ 2 - 10 & 1 & 6 & 6 \\ 11 - 19 & 3 & 15 & 45 \\ 20 - 28 & 9 & 24 & 216 \end{array}$

Step 4

Add the values in the $f \cdot M$ column.

$6 + 45 + 216 = 267$

Step 5

Add the values in the frequency column.

$n = 1 + 3 + 9 = 13$

Step 6

The mean (mu) is the sum of $f \cdot M$ divided by $n$ , which is the sum of frequencies.

$μ = \frac{\sum_{}^{} f \cdot M}{\sum_{}^{} f}$

Step 7

The mean is the sum of the product of the midpoints and frequencies divided by the total of frequencies.

$μ = \frac{267}{13}$

Step 8

Simplify the right side of $μ = \frac{267}{13}$ .

$20.53846153$