Statistics Examples

\begin{matrix} Class & Frequency 360 - 369 & 2 370 - 379 & 3 380 - 389 & 5 390 - 399 & 7 400 - 409 & 5 410 - 419 & 4 420 - 429 & 4 430 - 439 & 1 \end{matrix}

$\begin{array}{c} Class & Frequency \\ 360 - 369 & 2 \\ 370 - 379 & 3 \\ 380 - 389 & 5 \\ 390 - 399 & 7 \\ 400 - 409 & 5 \\ 410 - 419 & 4 \\ 420 - 429 & 4 \\ 430 - 439 & 1 \end{array}$

Step 1

Find the midpoint

M

$M$ for each class.

\begin{matrix} Class & Frequency (f) & Midpoint (M) 360 - 369 & 2 & 364.5 370 - 379 & 3 & 374.5 380 - 389 & 5 & 384.5 390 - 399 & 7 & 394.5 400 - 409 & 5 & 404.5 410 - 419 & 4 & 414.5 420 - 429 & 4 & 424.5 430 - 439 & 1 & 434.5 \end{matrix}

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) \\ 360 - 369 & 2 & 364.5 \\ 370 - 379 & 3 & 374.5 \\ 380 - 389 & 5 & 384.5 \\ 390 - 399 & 7 & 394.5 \\ 400 - 409 & 5 & 404.5 \\ 410 - 419 & 4 & 414.5 \\ 420 - 429 & 4 & 424.5 \\ 430 - 439 & 1 & 434.5 \end{array}$

Step 2

Multiply the frequency of each class by the class midpoint.

\begin{matrix} Class & Frequency (f) & Midpoint (M) & f \cdot M 360 - 369 & 2 & 364.5 & 2 \cdot 364.5 370 - 379 & 3 & 374.5 & 3 \cdot 374.5 380 - 389 & 5 & 384.5 & 5 \cdot 384.5 390 - 399 & 7 & 394.5 & 7 \cdot 394.5 400 - 409 & 5 & 404.5 & 5 \cdot 404.5 410 - 419 & 4 & 414.5 & 4 \cdot 414.5 420 - 429 & 4 & 424.5 & 4 \cdot 424.5 430 - 439 & 1 & 434.5 & 1 \cdot 434.5 \end{matrix}

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) & f \cdot M \\ 360 - 369 & 2 & 364.5 & 2 \cdot 364.5 \\ 370 - 379 & 3 & 374.5 & 3 \cdot 374.5 \\ 380 - 389 & 5 & 384.5 & 5 \cdot 384.5 \\ 390 - 399 & 7 & 394.5 & 7 \cdot 394.5 \\ 400 - 409 & 5 & 404.5 & 5 \cdot 404.5 \\ 410 - 419 & 4 & 414.5 & 4 \cdot 414.5 \\ 420 - 429 & 4 & 424.5 & 4 \cdot 424.5 \\ 430 - 439 & 1 & 434.5 & 1 \cdot 434.5 \end{array}$

Step 3

Simplify the

f \cdot M

$f \cdot M$ column.

\begin{matrix} Class & Frequency (f) & Midpoint (M) & f \cdot M 360 - 369 & 2 & 364.5 & 729 370 - 379 & 3 & 374.5 & 1123.5 380 - 389 & 5 & 384.5 & 1922.5 390 - 399 & 7 & 394.5 & 2761.5 400 - 409 & 5 & 404.5 & 2022.5 410 - 419 & 4 & 414.5 & 1658 420 - 429 & 4 & 424.5 & 1698 430 - 439 & 1 & 434.5 & 434.5 \end{matrix}

$\begin{array}{c} Class & Frequency (f) & Midpoint (M) & f \cdot M \\ 360 - 369 & 2 & 364.5 & 729 \\ 370 - 379 & 3 & 374.5 & 1123.5 \\ 380 - 389 & 5 & 384.5 & 1922.5 \\ 390 - 399 & 7 & 394.5 & 2761.5 \\ 400 - 409 & 5 & 404.5 & 2022.5 \\ 410 - 419 & 4 & 414.5 & 1658 \\ 420 - 429 & 4 & 424.5 & 1698 \\ 430 - 439 & 1 & 434.5 & 434.5 \end{array}$

Step 4

Add the values in the

f \cdot M

$f \cdot M$ column.

729 + 1123.5 + 1922.5 + 2761.5 + 2022.5 + 1658 + 1698 + 434.5 = 12349.5

$729 + 1123.5 + 1922.5 + 2761.5 + 2022.5 + 1658 + 1698 + 434.5 = 12349.5$

Step 5

Add the values in the frequency column.

n = 2 + 3 + 5 + 7 + 5 + 4 + 4 + 1 = 31

$n = 2 + 3 + 5 + 7 + 5 + 4 + 4 + 1 = 31$

Step 6

The mean (mu) is the sum of

f \cdot M

$f \cdot M$ divided by

n

$n$ , which is the sum of frequencies.

μ = \frac{\sum f \cdot M}{\sum f}

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

Step 7

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

μ = \frac{12349.5}{31}

$μ = \frac{12349.5}{31}$

Step 8

Simplify the right side of

μ = \frac{12349.5}{31}

$μ = \frac{12349.5}{31}$ .

398.37096774

$398.37096774$