Q.2.86 - Elementary Statistics

Question

The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed about $33.5\mathrm{lb}$ of cheese in 2011. Cheese consumption has increased steadily since 1960 , when the average American ate only $8.3\mathrm{lb}$ of cheese annually. The following table provides last year's cheese consumption, in pounds, for 35 randomly selected Americans. Use limit grouping with a first class of $20-22$ and a class width of 3 .

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).

Step-by-Step Solution

Answer

(a)

$\begin{array}{|ll|}\hline \text{ Class limit }& \text{ Frequency }\\ 20-22& 1\\ 23-25& 3\\ 26-28& 5\\ 29-31& 3\\ 32-34& 5\\ 36-37& 9\\ 38-40& 2\\ 41-43& 4\\ 44-46& 3\\ \text{ Total }& 35\\ \hline\end{array}$

(b)

$\begin{array}{|lllll|}\hline \text{ Class limits }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}& & \\ 20-22& 1& 1/35& =& 0.0286\\ 23-25& 3& 3/35& =& 0.0857\\ 26-28& 5& 5/35& =& 0.1429\\ 29-31& 3& 3/35& =& 0.0857\\ 32-34& 5& 5/35& =& 0.1429\\ 35-37& 9& 9/35& =& 0.2571\\ 38-40& 2& 2/35& =& 0.0571\\ 41-43& 4& 4/35& =& 0.1143\\ 44-46& 3& 3/35& =& 0.0857\\ \text{ Total }& 35& & =& 1\\ \hline\end{array}$

(c) 

(d)

Part (a)Step 1: Given information

Given in the question that, The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed about $33.5 \mathrm{lb}$ of cheese in 2011. Cheese consumption has increased steadily since 1960 , when the average American ate only $8.3 \mathrm{lb}$ of cheese annually. The following table provides last year's cheese consumption, in pounds, for 35 randomly selected Americans. Use limit grouping with a first class of $20-22$ and a class width of 3 .

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:

$\begin{array}{|ll|}\hline \text{ Class limit }& \text{ Frequency }\\ 20-22& 1\\ 23-25& 3\\ 26-28& 5\\ 29-31& 3\\ 32-34& 5\\ 36-37& 9\\ 38-40& 2\\ 41-43& 4\\ 44-46& 3\\ \text{ Total }& 35\\ \hline\end{array}$

Part(b) Step 1: Given information

Given in the question that, The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed about $33.5\mathrm{lb}$ of cheese in 2011. Cheese consumption has increased steadily since 1960 , when the average American ate only $8.3\mathrm{lb}$ of cheese annually. The following table provides last year's cheese consumption, in pounds, for 35 randomly selected Americans. Use limit grouping with a first class of $20-22$ and a class width of 3 .

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:

$\begin{array}{|lllll|}\hline \text{ Class limits }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}& & \\ 20-22& 1& 1/35& =& 0.0286\\ 23-25& 3& 3/35& =& 0.0857\\ 26-28& 5& 5/35& =& 0.1429\\ 29-31& 3& 3/35& =& 0.0857\\ 32-34& 5& 5/35& =& 0.1429\\ 35-37& 9& 9/35& =& 0.2571\\ 38-40& 2& 2/35& =& 0.0571\\ 41-43& 4& 4/35& =& 0.1143\\ 44-46& 3& 3/35& =& 0.0857\\ \text{ Total }& 35& & =& 1\\ \hline\end{array}$

Part(c) Step 1: Given information

Given in the question that, The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed about $33.5\mathrm{lb}$of cheese in 2011. Cheese consumption has increased steadily since 1960 , when the average American ate only $8.3\mathrm{lb}$ of cheese annually. The following table provides last year's cheese consumption, in pounds, for 35 randomly selected Americans. Use limit grouping with a first class of $20-22$ and a class width of 3 .

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 be of the same width and must be bordered by the lower class limits.

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

The frequency distribution histogram is shown below:

Part(d) Step 1: Given information

Given in the question that, The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed about$33.5\mathrm{lb}$of cheese in 2011. Cheese consumption has increased steadily since 1960 , when the average American ate only $8.3\mathrm{lb}$ of cheese annually. The following table provides last year's cheese consumption, in pounds, for 35 randomly selected Americans. Use limit grouping with a first class of $20-22$ and a class width of 3 .

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: