Find Class Midpoints ($x_i$)

Calculate the midpoint for each class interval using the formula $x_i = \frac{\text{Lower limit} + \text{Upper limit}}{2}$. For 10⁻²⁰ it is 15, for 20-30 it is 25, for 30-40 it is 35, and for 40-50 it is 45.

$x_i = \{15, 25, 35, 45\}$

Calculate $f_i x_i$ Products

Multiply each frequency ($f_i$) by its respective class midpoint ($x_i$): $5 \times 15 = 75$, $10 \times 25 = 250$, $15 \times 35 = 525$, and $10 \times 45 = 450$.

$f_i x_i = \{75, 250, 525, 450\}$

Sum Frequencies and Products

Find the total sum of frequencies $\sum f_i = 5 + 10 + 15 + 10 = 40$ and the total sum of products $\sum f_i x_i = 75 + 250 + 525 + 450 = 1300$.

$\sum f_i = 40, \quad \sum f_i x_i = 1300$

Compute Arithmetic Mean

Apply the arithmetic mean formula for grouped data by dividing the total product sum by the total frequency sum: $1300 / 40 = 32.5$.

$\overline{x} = \frac{1300}{40} = 32.5$