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?

Question

0 0 0 0 0 0 0 0 0 1 1 2 3 3 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 8 8 8 9 (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 the histogram with 10 classes, we can use the digits from 0 to 9, since we are interested in the last digits of the heights in centimeters. The data given consists of the last digits of heights as follows:

• 0: 10 occurrences
• 1: 2 occurrences
• 2: 1 occurrence
• 3: 3 occurrences
• 4: 1 occurrence
• 5: 10 occurrences
• 6: 2 occurrences
• 7: 0 occurrences
• 8: 3 occurrences
• 9: 1 occurrence

Now, we can summarize this data in terms of a table with the digits (0 to 9) and the corresponding frequency:

| Digit | Frequency | |-------|-----------| | 0 | 10 | | 1 | 2 | | 2 | 1 | | 3 | 3 | | 4 | 1 | | 5 | 10 | | 6 | 2 | | 7 | 0 | | 8 | 3 | | 9 | 1 |

To visualize this, the histogram would show a clear peak at 0 and 5, indicating higher frequencies for those last digits compared to the others.

Conclusion from the distribution

Looking at the frequency of the last digits, option a is indeed a valid conclusion. The digits of 0 and 5 occur disproportionately more often than the others, indicating a potential bias in the reporting of the heights, as certain digits are favored:

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

Thus, the most suitable answer is a.