(a) To draw the histogram, calculate the frequency density for each class interval using the formula:

\(\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}\)

Class widths: 5, 5, 10, 20, 30

Frequency densities: \(\frac{10}{5} = 2\), \(\frac{5}{5} = 1\), \(\frac{26}{10} = 2.6\), \(\frac{32}{20} = 1.6\), \(\frac{18}{30} = 0.6\)

Draw bars with these heights for each class interval.

(b) The lower quartile (LQ) is in the 11 – 20 interval, and the upper quartile (UQ) is in the 21 – 40 interval. The greatest possible interquartile range (IQR) is:

\(40 - 11 = 29\)

(c) To estimate the mean, calculate the midpoint of each class interval:

Midpoints: 3, 8, 15.5, 30.5, 55.5

Calculate the mean using:

\(\text{Mean} = \frac{3 \times 10 + 8 \times 5 + 15.5 \times 26 + 30.5 \times 32 + 55.5 \times 18}{91}\)

\(= \frac{30 + 40 + 403 + 976 + 999}{91}\)

\(= \frac{2448}{91} \approx 26.9\)