Q. 26 - Elementary Statistics

Question

Latent Fingerprints. Firearms, live ammunition, and spent cartridge casings are often submitted to crime laboratories to be processed for latent fingerprints. B. Maldonado explored the chances of successfully recovering fingerprints in the article, "Study on Developing Latent Fingerprints on Firearm Evidence" (Journal of Forensic identification, Vol. 62, Issue 5, pp. 425-429). The following table provides a frequency distribution for the type of evidence submitted to crime laboratories over a 2-year period at the Denver Police Department.

Evidence	Frequency
Firearm	289
Magazine	161
Live Cartridge	2727
Spent Cartridge Casing	259

a) Obtain a relative-frequency distribution.

b) Draw a pie chart.

c) Construct a bar chart.

d) Interpret your results.

 

Step-by-Step Solution

Answer

Ans:  

(a)  

Evidence	Frequency	Relative frequency
Firearm	289	0.084
Magazine	161	0.047
Live cartridge	2.727	0.794
Spent cartridge casing	259	0.075
	3,436	1

(b)   

(c)    

(d)   From the pie chart above, it is clear that the "Live cartridge" evidence covers a large part of the circle. Also, from the bar chart, it is clear that the "Live Cartridge" evidence has a very high line representing "live cartridge". Therefore, it can be concluded that the most common type of evidence sent is $79.4\%$ of the time "live cartridge".

Step 1. Given information.

given,

      

Evidence	Frequency
Firearm	289
Magazine	161
Live Cartridge	2727
Spent Cartridge Casing	259

Step 2. Find the relative frequency distribution.

The relative frequency is found using the formula, 

   $Relative frequency = \frac{Frequency}{Number of observations}$

Thus, the relative frequency distribution is given below:

   

Evidence	Frequency	Relative frequency
Firearm	289	0.084
Magazine	161	0.047
Live cartridge	2,727	0.794
Spent cartridge casing	259	0.075
	3,436	1

Step 3. (b) Use Minitab to create a pie chart.

In the pie chart, half of each class is obtained by multiplying $360 degrees$ and its corresponding frequency waves.

MINITAB process:

Step 1) Select Graph> Pie Chart.

Step 2) Select the chart values in the table.

Step 3) Select EVIDENCE under Category Variability.

Step 4) Select FREQUENCY under variable

Step 5) Select Labels and Select the Slides Labels tab.

Step 6) Check the category name and percentage below the label pie pieces.

Step 7) Click OK.

Step 4. Minitab output,

Step 5. (c) Use Minitab to create a bar chart.

MINITAB process:

Step 1) Select Graph> Bar Chart

Step 2) In the representative bars, select the values in the table

Step 3) Select Easy, then click OK.

Step 4) For graph variables, select the FREQUENCY column.

Step 4) In the Structure Variation, enter one column EVIDENCE.

Step 5) Select chart options.

Step 6) Check Show Y As a Percentage.

Step 7) Click OK.

Step 6. Minitab Output,

Step 7. (d) Description,

 From the pie chart above, it is clear that the "Live cartridge" evidence covers a large part of the circle. Also, from the bar chart, it is clear that the "Live Cartridge" evidence has a very high line representing "live cartridge".  

Therefore, it can be concluded that the most common type of evidence sent is $79.4\%$ of the time "live cartridge".