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:
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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.
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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.
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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.
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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.
3 answers