Question

Consumer Reports provides information on new automobile models, including price, mileage ratings, engine size, body size, and indicators of features. A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons. Use cutpoint grouping with 12 as the first cutpoint and classes of equal width 2 .

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result from part (b).

Short answer

(a)

$\begin{array}{|lll|}\hline \text{Class}& \text{Frequency}& \begin{array}{l}\text{Relative}\\ \text{frequency}\end{array}\\ 12<14& 2& 0.057\\ 14<16& 6& 0.171\\ 16<18& 7& 0.2\\ 18<20& 6& 0.171\\ 20<22& 6& 0.171\\ 22<24& 3& 0.086\\ 24<26& 3& 0.086\\ 26<28& 2& 0.057\\ \text{Total}& 35& 1\\ \hline\end{array}$

(b)

$\begin{array}{|lll|}\hline \text{Class}& \text{Frequency}& \begin{array}{l}\text{Relative}\\ \text{frequency}\end{array}\\ 12<14& 2& 0.057\\ 14<16& 6& 0.171\\ 16<18& 7& 0.2\\ 18<20& 6& 0.171\\ 20<22& 6& 0.171\\ 22<24& 3& 0.086\\ 24<26& 3& 0.086\\ 26<28& 2& 0.057\\ \text{Total}& 35& 1\\ \hline\end{array}$

(c)

(d)

Step-by-step solution

Part (a)Step 1: Given information

Consumer Reports provides information on new automobile models, including price, mileage ratings, engine size, body size, and indicators of features. A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons. Use cutpoint grouping with 12 as the first cutpoint and classes of equal width 2 .

We need to determine a frequency distribution.

Part(a) Step 2: Explanation

The given data is,

The number of values that fall between the class's bounds is the frequency.

The data's frequency distribution is as follows:

$\begin{array}{|lll|}\hline \text{Class}& \text{Frequency}& \begin{array}{l}\text{Relative}\\ \text{frequency}\end{array}\\ 12<14& 2& 0.057\\ 14<16& 6& 0.171\\ 16<18& 7& 0.2\\ 18<20& 6& 0.171\\ 20<22& 6& 0.171\\ 22<24& 3& 0.086\\ 24<26& 3& 0.086\\ 26<28& 2& 0.057\\ \text{Total}& 35& 1\\ \hline\end{array}$

Part(b) Step 1: Given information

Consumer Reports provides information on new automobile models, including price, mileage ratings, engine size, body size, and indicators of features. A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons. Use cutpoint grouping with 12 as the first cutpoint and classes of equal width 2 .

We need to obtain a relative-frequency distribution.

Part (b) Step 2: Explanation

The given data is,

The frequency is divided by the overall frequency to get the relative frequency.

The data's relative frequency distribution is as follows:

$\begin{array}{|lll|}\hline \text{Class}& \text{Frequency}& \begin{array}{l}\text{Relative}\\ \text{frequency}\end{array}\\ 12<14& 2& 0.057\\ 14<16& 6& 0.171\\ 16<18& 7& 0.2\\ 18<20& 6& 0.171\\ 20<22& 6& 0.171\\ 22<24& 3& 0.086\\ 24<26& 3& 0.086\\ 26<28& 2& 0.057\\ \text{Total}& 35& 1\\ \hline\end{array}$

Part(c) Step 1: Given information

Consumer Reports provides information on new automobile models, including price, mileage ratings, engine size, body size, and indicators of features. A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons. Use cutpoint grouping with 12 as the first cutpoint and classes of equal width 2 .

We need to construct a frequency histogram based on the result from part (a)

Part(c) Step 2: Explanation

The given data is,

On a horizontal axis, the histogram shows the quantitative data classes, and on a vertical axis, the frequencies of those classes.

The bars must all be the same width and must be bordered by the lower class limitations.

The frequency must be represented by the height of the bars.

The frequency distribution histogram is shown below:

Part(d) Step 1: Given information

Consumer Reports provides information on new automobile models, including price, mileage ratings, engine size, body size, and indicators of features. A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons. Use cutpoint grouping with 12 as the first cutpoint and classes of equal width 2 .

We need to construct a relative-frequency histogram based on the result from part (b)

Part(d) Step 2: Explanation

The given data is,

On a horizontal axis, the histogram shows the quantitative data classes, and on a vertical axis, the frequencies of those classes.

The bars must all be the same width and must be bordered by the lower class limitations.

The frequency must be represented by the height of the bars.

The relative frequency distribution histogram is shown below: