The problem provides a table of heights and their corresponding frequencies. We need to calculate the frequency density for each class and then determine which of the given histograms (A, B, C, or D) correctly represents the data.

1. Problem Description

The problem provides a table of heights and their corresponding frequencies. We need to calculate the frequency density for each class and then determine which of the given histograms (A, B, C, or D) correctly represents the data.

2. Solution Steps

First, we need to calculate the class widths and frequency densities for each class.

Frequency density is calculated as frequency divided by class width.

Class 1: $0 < h \le 10$

Class width = $10 - 0 = 10$

Frequency = 22

Frequency density = $22 / 10 = 2.2$

Class 2: $10 < h \le 15$

Class width = $15 - 10 = 5$

Frequency = 17

Frequency density = $17 / 5 = 3.4$

Class 3: $15 < h \le 30$

Class width = $30 - 15 = 15$

Frequency = 6

Frequency density = $6 / 15 = 0.4$

Now we look at the histograms.

Histogram A: Frequency densities are approximately

0. 8, 3, and 2.8

Histogram B: Frequency densities are approximately

0. 8, 3, and 2.8

Histogram C: Frequency densities are approximately 2.2, 3.4, and 0.4

Histogram D: Frequency densities are approximately 2.2, 3.4, and a value larger than 0, maybe about

1.

The frequency densities for each class are: 2.2, 3.4, and 0.

4. Comparing these with the histograms, we see that histogram C matches these values.

3. Final Answer

C