Chapter 11: Q. 2 (page 631)
The rightmost bar of the histogram above appears to be twice as long as any of the other bars. Is the frequency of the 10-12 interval twice as great as the frequency of any other interval? Explain.
Short Answer
The frequency of the interval 10-12 is not twice as great as the frequency of any other interval.
Step by step solution
Step 1. Given Information.
The histogram is shown below.
The rightmost bar of the histogram appears to be twice as long as any of the other bars.
Step 2. Explanation.
Consider, the histogram given:
The histogram has a broken vertical axis. The broken vertical axis exaggerates the differences in the bar lengths.
The bar corresponding to the interval 10-12 appears to be the tallest.
The bar corresponding to the interval 1-3 appears to be the next tallest.
Compare the frequency of the intervals 1-3 and 10-12.
The frequency of the interval 1-3 appears to be somewhere between 165-170 whereas the frequency of the interval 10-12 appears to be somewhere between 185-190.
The approximate difference between the frequencies of the two intervals is 20. Hence the frequency of the interval 10-12 is not twice as great as the frequency of the interval 1-3.
Similarly, compare the frequency of the intervals 4-6 and 10-12.
The frequency of the interval 4-6 appears to be somewhere between 160-165.
The approximate difference between the frequencies of the two intervals (4-6 and 10-12) is 25. Hence, the frequency of the interval 10-12 is not twice as great as the frequency of the interval 4-6.
Now, compare the frequency of the intervals 7-9 and 10-12.
The frequency of the interval 7-9 appears to be 160.
The approximate difference between the frequencies of the two intervals (7-9 and 10-12) is 25-30. Hence, the frequency of the interval 10-12 is not twice as great as the frequency of the interval 7-9.
Therefore, the rightmost bar may appear twice as long as any of the bars but its corresponding frequency is not twice as great as the frequency of any other interval.
That is the frequency of the interval 10-12 is not twice as great as the frequency of any other interval.
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