The following frequency distribution table gives the ages of 200 patients treated in a hospital in a week. Find the mode of ages of the patients.

Answer: Mode ≈ 12.31 years

The classes are not continuous, so make them continuous: 5–9 becomes 4.5–9.5, 10–14 becomes 9.5–14.5, and so on.

The highest frequency is 50, so the modal class is 9.5–14.5.

\(L = 9.5\), \(f_1 = 50\), \(f_0 = 32\), \(f_2 = 36\), \(h = 5\)

\[ \text{Mode} = L + \left[\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right] \times h \]

\[ = 9.5 + \frac{50 - 32}{100 - 32 - 36} \times 5 \]

\[ = 9.5 + \frac{18}{32} \times 5 \approx 12.31 \]