Statistics Examples

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

Step 1

Find the midpoint $M$ for each class.

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

Step 2

Multiply the frequency of each class by the class midpoint.

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

Step 3

Simplify the $f \cdot M$ column.

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) & f \cdot M \\ 12 - 14 & 4 & 13 & 52 \\ 15 - 17 & 5 & 16 & 80 \\ 19 - 21 & 9 & 20 & 180 \\ 22 - 24 & 2 & 23 & 46 \end{array}$

Step 4

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

$52 + 80 + 180 + 46 = 358$

Step 5

Add the values in the frequency column.

$n = 4 + 5 + 9 + 2 = 20$

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.

$μ = \frac{358}{20}$

Step 8

Simplify the right side of $μ = \frac{358}{20}$ .

$17.9$

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