Chapter 11.3, Problem 2C

To determine

To explain: whether the frequency of the given interval is twice as great as the frequency of any other interval.

Answer to Problem 2C

The frequencyof the interval $10-12$ is not twice as great as the frequency of any other interval.

Explanation of Solution

Given information:

The given information:

The histogram:

  

The rightmost bar of the histogram appears to be twice as long as any of the other bars.

The interval of the bar is $10-12$ .

As per the question,

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 $165-170$ where as 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, thefrequency 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 frequencyof the interval $10-12$ is not twice as great as the frequency of any other interval.