Draw a histogram and use it to estimate the mode to the nearest whole number.

• Plot the class boundaries on the horizontal (x) axis. The given class boundaries are 15.5, 18.5, 21.5, 24.5, 27.5, and 30.5.
• Plot the frequencies on the vertical (y) axis.
• Draw rectangular bars for each class interval. The width of each bar should span its respective class boundaries, and the height of each bar should correspond to its frequency. For example, the first bar would span from 15.5 to 18.5 on the x-axis and have a height of 18 on the y-axis.

(As an AI, I cannot physically draw the histogram for you, but I will proceed with the calculation which is derived from the graphical method.)

The modal class is the class interval with the highest frequency. From the table:

• 16 - 18: Frequency = 18
• 19 - 21: Frequency = 30
• 22 - 24: Frequency = 35 (This is the highest frequency)
• 25 - 27: Frequency = 24
• 28 - 30: Frequency = 13 The modal class is $22 - 24$, with class boundaries $21.5 - 24.5$.

The formula for the mode of grouped data, which is derived from the graphical estimation method, is:

Where:

• $L$ = lower class boundary of the modal class = 21.5
• $f_m$ = frequency of the modal class = 35
• $f_1$ = frequency of the class before the modal class = 30
• $f_2$ = frequency of the class after the modal class = 24
• $w$ = class width = $18.5 - 15.5 = 3$

Substitute the values into the formula:

Rounding 22.4375 to the nearest whole number gives 22.