To estimate the mean, we first find the midpoints of each class interval:

• 1 – 25: midpoint = 13
• 26 – 35: midpoint = 30.5
• 36 – 45: midpoint = 40.5
• 46 – 55: midpoint = 50.5
• 56 – 90: midpoint = 73

Next, we calculate the mean using the formula:

\(\bar{x} = \frac{\sum f x}{\sum f} = \frac{4 \times 13 + 24 \times 30.5 + 38 \times 40.5 + 34 \times 50.5 + 20 \times 73}{120} = \frac{5500}{120} = 45.8\)

\(To find the variance, we use:\)

\(s^2 = \frac{\sum f x^2}{\sum f} - \bar{x}^2\)

\(\sum f x^2 = 4 \times 13^2 + 24 \times 30.5^2 + 38 \times 40.5^2 + 34 \times 50.5^2 + 20 \times 73^2 = 278620\)

\(s^2 = \frac{278620}{120} - 45.8^2 = 2321.8333 - 2097.64 = 224.1933\)

The standard deviation is:

\(s = \sqrt{224.1933} = 14.9\)