Q. 31 - Elementary Statistics

Question

In problem 31-33,

a. Identify the population and variable under consideration.

b. use the technology of your choice to obtain and interpret a frequency histogram, a relative-frequency histogram, or a percent histogram of the data. 

c. use the technology of your choice to obtain a dotplot of the data. 

d. use the technology of your choice to obtain a stem-and-leaf diagram of the data. 

e. identify the modality and symmetry (or nonsymmetry) of the distribution. 

f. if the distribution is unimodal and nonsymmetric, state whether it is right skewed or left skewed.

31. Agricultural Exports. The U.S. Department of Agriculture collects data pertaining to the value of agricultural exports and publishes its findings in U.S. Agricultural Trade Update. For one year, the values of these exports, by state, are provided on the WeissStats site. Data are in millions of dollars.

Step-by-Step Solution

Answer

(a) The population is the states in US and variable is export. 

(b) A frequency and a relative-frequency as:

(c) A dotplot of the data as:

(d) A stem-and-leaf diagram of the data as:

(e) The distribution is unimodal and nonsymmetric 

(f) The distribution is right skewed.

Part (a) Step 1: Given information

To identify the population and variable under consideration.

Part (a) Step 2: Explanation

In a dot plot, a dot is placed above the relevant number on the number line for each piece of data.
As a result, the population consists of the states in US and variable is export.

Part (b) Step 1: Given information

To use the technology of choice to obtain and interpret a frequency histogram, a relative-frequency histogram, or a percent histogram of the data.

Part (b) Step 2: Explanation

The number of data values that fall into a class is known as frequency. The majority of states have exports ranging from 0 to 1000 million dollars.
The frequency and relative frequency is calculated as follows:

Part (c) Step 1: Given information

To use the technology of your choice to obtain a dotplot of the data.

Part (c) Step 2: Explanation

The number of data values that fall into a class is known as frequency. Place a dot above the corresponding number on the number line for each data value. Obtain a dotplot of the data as:

Part (d) Step 1: Given information

To use the technology of your choice to obtain a stem-and-leaf diagram of the data

Part (d) Step 2: Explanation

The number of data values that fall into a class is known as frequency. All data should be rounded to the closest hundredth.
Make a horizontal line. Place the thousand digits to the left of the vertical line and the hundreds digits to the right of the vertical line for each data value. To obtain a stem-and-leaf diagram of the data as:

Part (e) Step 1: Given information

To identify the modality and symmetry (or nonsymmetry) of the distribution.

Part (e) Step 2: Explanation

Since, there is only one peak in the histogram, the distribution is unimodal.
Because the single peak in the histogram is to the left, the distribution is non-symmetric.
As a result, the distribution is unimodal and nonsymmetric.

Part (f) Step 1: Given information

To state the distribution is unimodal and nonsymmetric, whether it is right skewed or left skewed.

Part (f) Step 2: Explanation

The number of data values that fall into a class is known as frequency. Because the top bar in the histogram is to the left, the distribution is right skewed.

As a result, the distribution is unimodal and nonsymmetric, it is right skewed.