Finite Math Examples

$\begin{array}{c} x & y \\ 1.95 - 2.15 & 19 \\ 2.15 - 2.35 & 19 \\ 2.35 - 2.55 & 17 \\ 2.55 - 2.75 & 14 \\ 2.75 - 2.95 & 9 \\ 2.95 - 3.15 & 7 \\ 3.15 - 3.35 & 4 \\ 3.35 - 3.55 & 4 \\ 3.55 - 3.75 & 3 \\ 3.75 - 3.95 & 1 \end{array}$

Step 1

Find the midpoint $M$ for each class.

$\begin{array}{c} x & y & Midpoint (M) \\ 1.95 - 2.15 & 19 & 2.05 \\ 2.15 - 2.35 & 19 & 2.25 \\ 2.35 - 2.55 & 17 & 2.45 \\ 2.55 - 2.75 & 14 & 2.65 \\ 2.75 - 2.95 & 9 & 2.85 \\ 2.95 - 3.15 & 7 & 3.05 \\ 3.15 - 3.35 & 4 & 3.25 \\ 3.35 - 3.55 & 4 & 3.45 \\ 3.55 - 3.75 & 3 & 3.65 \\ 3.75 - 3.95 & 1 & 3.85 \end{array}$

Step 2

Multiply the frequency of each class by the class midpoint.

$\begin{array}{c} x & y & Midpoint (M) & f \cdot M \\ 1.95 - 2.15 & 19 & 2.05 & 19 \cdot 2.05 \\ 2.15 - 2.35 & 19 & 2.25 & 19 \cdot 2.25 \\ 2.35 - 2.55 & 17 & 2.45 & 17 \cdot 2.45 \\ 2.55 - 2.75 & 14 & 2.65 & 14 \cdot 2.65 \\ 2.75 - 2.95 & 9 & 2.85 & 9 \cdot 2.85 \\ 2.95 - 3.15 & 7 & 3.05 & 7 \cdot 3.05 \\ 3.15 - 3.35 & 4 & 3.25 & 4 \cdot 3.25 \\ 3.35 - 3.55 & 4 & 3.45 & 4 \cdot 3.45 \\ 3.55 - 3.75 & 3 & 3.65 & 3 \cdot 3.65 \\ 3.75 - 3.95 & 1 & 3.85 & 1 \cdot 3.85 \end{array}$

Step 3

Simplify the $f \cdot M$ column.

$\begin{array}{c} x & y & Midpoint (M) & f \cdot M \\ 1.95 - 2.15 & 19 & 2.05 & 38.94\overline{9} \\ 2.15 - 2.35 & 19 & 2.25 & 42.75 \\ 2.35 - 2.55 & 17 & 2.45 & 41.65 \\ 2.55 - 2.75 & 14 & 2.65 & 37.1 \\ 2.75 - 2.95 & 9 & 2.85 & 25.65 \\ 2.95 - 3.15 & 7 & 3.05 & 21.34\overline{9} \\ 3.15 - 3.35 & 4 & 3.25 & 13 \\ 3.35 - 3.55 & 4 & 3.45 & 13.8 \\ 3.55 - 3.75 & 3 & 3.65 & 10.95 \\ 3.75 - 3.95 & 1 & 3.85 & 3.85 \end{array}$

Step 4

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

$38.94\overline{9} + 42.75 + 41.65 + 37.1 + 25.65 + 21.34\overline{9} + 13 + 13.8 + 10.95 + 3.85 = 249.04\overline{9}$

Step 5

Add the values in the frequency column.

$n = 19 + 19 + 17 + 14 + 9 + 7 + 4 + 4 + 3 + 1 = 97$

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.

$μ = \frac{249.04\overline{9}}{97}$

Step 8

Simplify the right side of $μ = \frac{249.04\overline{9}}{97}$ .

$2.56752577$