Q.2.36 - Elementary Statistics

Question

Drug dealer motivation is traditionally attributed to greed or social pressures. Researchers R. Highland and D. Dabney explore possible personality characteristics as a motivation in the article "Using Adlerian Theory to Shed Light on Drug Dealer Motivations" (Applied Psychology in Criminal Justice, Vol. 5, Issue 2, pp. 109-138). The following table lists the types of drug sold from a sample of convicted drug dealers.

Step-by-Step Solution

Answer

(a) The relative frequency distribution

(b) Pie chart

(c) Bar chart

Part (a): Step 1: Given information

Given in the question that, Drug dealer motivation is traditionally attributed to greed or social pressures. Researchers R. Highland and D. Dabney explore possible personality characteristics as a motivation in the article "Using Adlerian Theory to Shed Light on Drug Dealer Motivations" (Applied Psychology in Criminal Justice, Vol. 5, Issue 2, pp. 109-138). The following table lists the types of drug sold from a sample of convicted drug dealers.

We need to obtain a relative -frequency Distribution.

Part(a) Step 2: Explanation

The relative frequency table is:

Drug sold	Frequency Relative	frequency
Marijuana	$73$	$0.3230$
Crack cocaine	$62$	$0.2743$
Powder cocaine	$45$	$0.1991$
Ecstasy	$20$	$0.0885$
Methamphetamine	$17$	$0.0752$
Heroin	$5$	$0.0221$
Other	$4$	$0.0177$
Total	$226$	$1.0000$

The general formula for the relative frequency is,

$\text{ Relative Frequency }=\frac{\text{ Frequency }}{\text{ Total frequency }}$

Substituting$"73"$ as the class level drug sold frequency and $" 226 "$ as the total number of class level drug sold frequency in relative frequency.

Relative Frequency of sold drug marijuana $=\frac{73}{226}$

                                                                        $=0.3230$

Part (a) Step 3: The relative frequency

Similarly, the relative frequency for the remaining faculty rankings are as follows:

Drug sold	Frequency Relative	frequency
Marijuana	$73$	$0.3230$
Crack cocaine	$62$	$0.2743$
Powder cocaine	$45$	$0.1991$
Ecstasy	$20$	$0.0885$
Methamphetamine	$17$	$0.0752$
Heroin	$5$	$0.0221$
Other	$4$	$0.0177$
Total	$226$	$1.0000$

Part(b) Step 1: Given information

Given in the question that, Drug dealer motivation is traditionally attributed to greed or social pressures. Researchers R. Highland and D. Dabney explore possible personality characteristics as a motivation in the article "Using Adlerian Theory to Shed Light on Drug Dealer Motivations" (Applied Psychology in Criminal Justice, Vol. 5, Issue 2 , pp. 109-138). The following table lists the types of drug sold from a sample of convicted drug dealers.

We need to draw a pie chart.

Part (b) Step 2: Explanation

Output using MINITAB software is given below:

When the relative frequency is multiplied by the degree$360$ , the pie slice for each type for the robbery is obtained.

Determining the pie chart slice size for sold drug marijuana:

pie slice for sold drug marijuana $=0.3230\times 360$

                                                       $=116.28$

Similarly, the pie slices for the remaining types of sold drugs are obtained below:

Drug sold	Pie slice sizes
Marijuana	$116.28$
Crack cocaine	$98.76$
Powder cocaine	$71.68$
Ecstasy	$31.86$
Methamphetamine	$27.08$
Heroin	$7.96$
Other	$6.37$

Proportion is calculated by the product of relative frequency of each class with $100 .$

Proportion for sold drug marijuana $=$ relative frequency $\times 100$

                                                           $=0.3230\times 100$
                                                           $=32.3$

Part (b) Step 2: Proportion for the remaining sold drugs

Similarly, the proportion for the remaining sold drugs are obtained below:

Drug sold	Relative frequency	percent
Marijuana	$0.3230$	$32.3$
Crack cocaine	$0.2743$	$27.4$
Powder cocaine	$0.1991$	$19.9$
Ecstasy	$0.0885$	$8.8$
Methamphetamine	$0.0752$	$7.5$
Heroin	$0.0221$	$2.2$
Other	$0.0177$	$1.8$

Software procedure:

Step by step procedure to draw the pie chart using MINITAB software.

• Choose Graph > Pie Chart.
•  Enter the columns of drug sold in Categorical variables.
•  In Summary variables, enter the corresponding column.
•  Click OK.

Part (c) Step 1: Given information

Given in the question that, Drug dealer motivation is traditionally attributed to greed or social pressures. Researchers R. Highland and D. Dabney explore possible personality characteristics as a motivation in the article "Using Adlerian Theory to Shed Light on Drug Dealer Motivations" (Applied Psychology in Criminal Justice, Vol. 5, Issue 2, pp. 109-138). The following table lists the types of drug sold from a sample of convicted drug dealers.

We need to construct a bar chart.

Part (c) Step 2: Explanation

•  Output using MINITAB software is given below:

Software procedure:

Step by step procedure to draw the bar chart using MINITAB software.

•  From Bars represent, choose Values from a table.
•  Under One column of values, choose Simple. Click OK.
•  Choose Simple, and then click OK.
•  In Graph variables, enter the column of drug sold.
•  In Categorical variables, enter the column of percent.
•  Click OK.

Thus, the bar chart is constructed for the location of the cities.