Question

Heights, reported in centimeters, of students in one class were obtained for a study. The last digits of those heights are listed. Construct a histogram with 10 classes. What can you conclude from the distribution of the digits?

- **0**: 9 occurrences
- **1**: 2 occurrences
- **2**: 1 occurrence
- **3**: 3 occurrences
- **4**: 1 occurrence
- **5**: 15 occurrences
- **6**: 2 occurrences
- **7**: 0 occurrences
- **8**: 3 occurrences
- **9**: 1 occurrence
(1 point)

a. The digits of 0 and 5 occur disproportionately more often than the others; the heights could have been reported
b. The choice of 10 classes was a poor choice; nothing can be concluded from this histogram.
c. This is a small sample; a histogram is not an appropriate way to display the data.
d. The histogram shows a normal distribution and can be used to predict heights of other classes.

Answer 1

To construct a histogram based on the provided data, we'll create 10 classes based on the last digits of the heights. The last digits (from 0 to 9) will form the x-axis, and the frequency of each digit will be on the y-axis.

Here's the data presented in a frequency table:

| Last Digit | Frequency |
|------------|-----------|
| 0 | 9 |
| 1 | 2 |
| 2 | 1 |
| 3 | 3 |
| 4 | 1 |
| 5 | 15 |
| 6 | 2 |
| 7 | 0 |
| 8 | 3 |
| 9 | 1 |

Next, let's visualize this in a histogram. Each digit from 0 to 9 will have a bar corresponding to its frequency.

The histogram would show:

- Bar for 0: Height 9
- Bar for 1: Height 2
- Bar for 2: Height 1
- Bar for 3: Height 3
- Bar for 4: Height 1
- Bar for 5: Height 15
- Bar for 6: Height 2
- Bar for 7: Height 0
- Bar for 8: Height 3
- Bar for 9: Height 1

Based on this information and the heights represented by the last digits, we can draw some conclusions.

**Conclusion from the options:**

- **a. The digits of 0 and 5 occur disproportionately more often than the others; the heights could have been reported.** This statement is accurate as we see that the frequency of the digit 5 is significantly higher than the other digits.

- **b. The choice of 10 classes was a poor choice; nothing can be concluded from this histogram.** This is not accurate, as we are dealing with 10 distinct last digits.

- **c. This is a small sample; a histogram is not an appropriate way to display the data.** While the sample size might be small, the histogram does provide useful visual insights into the distribution of last digits.

- **d. The histogram shows a normal distribution and can be used to predict heights of other classes.** The distribution does not appear normal; instead, it shows a few significant peaks (especially at 5) and does not justify predicting other heights.

The most correct conclusion is **a. The digits of 0 and 5 occur disproportionately more often than the others; the heights could have been reported.**