Questions: (a) Is the shape of the histogram essentially bimodal? Yes, because the histogram has two peaks. No, because the histogram has two peaks. Yes, because the histogram has one peak. No, because the histogram has one peak. (b) Jose looked at the raw data and discovered that the 54 data values included both the city and Highway mileages for 27 cars. He used the city mileages for the 27 cars to make the Histogram below. Histogram of City mpg Using this information and the histograms shown above, construct a frequency table for the highway mileages of the same cars. Use class boundaries 16.5, 20.5, 24.5, 28.5, 32.5, 36.5, and 40.5.

(a) Is the shape of the histogram essentially bimodal?
Yes, because the histogram has two peaks.
No, because the histogram has two peaks.
Yes, because the histogram has one peak.
No, because the histogram has one peak.
(b) Jose looked at the raw data and discovered that the 54 data values included both the city and Highway mileages for 27 cars. He used the city mileages for the 27 cars to make the Histogram below.

Histogram of City mpg

Using this information and the histograms shown above, construct a frequency table for the highway mileages of the same cars. Use class boundaries 16.5, 20.5, 24.5, 28.5, 32.5, 36.5, and 40.5.

Transcript text: (a) Is the shape of the histogram essentially bimodal? Yes, because the histogram has two peaks. No, because the histogram has two peaks. Yes, because the histogram has one peak. No, because the histogram has one peak. (b) Jose looked at the raw data and discovered that the 54 data values included both the city and Highway mileages for 27 cars. He used the city mileages for the 27 cars to make the Histogram below. Histogram of City mpg Using this information and the histograms shown above, construct a frequency table for the highway mileages of the same cars. Use class boundaries $16.5, 20.5, 24.5, 28.5, 32.5, 36.5$, and 40.5.

Solution

Solution Steps

Step 1: Determine if the first histogram is bimodal

A bimodal histogram has two distinct peaks. The first histogram (mpg) has two peaks, around 16.5 mpg and 32.5 mpg.

Step 2: Create a frequency table for highway mileages

The first histogram represents the combined city and highway mileages for 27 cars. The second histogram represents only the city mileages for those same 27 cars. We can find the frequencies for the highway mileages by subtracting the city mileage frequencies from the combined frequencies.

| Class Boundaries | Combined Frequency | City Frequency | Highway Frequency | |---|---|---|---| | 8.5-12.5 | 4 | 4 | 0 | | 12.5-16.5 | 17 | 17 | 0 | | 16.5-20.5 | 8 | 5 | 3 | | 20.5-24.5 | 3 | 1 | 2 | | 24.5-28.5 | 4 | 0 | 4 | | 28.5-32.5 | 13 | 0 | 13 | | 32.5-36.5 | 4 | 0 | 4 | | 36.5-40.5 | 1 | 0 | 1 |