Selecting the Most Appropriate Measure of Dispersion You are studying whether se

Question

Selecting the Most Appropriate Measure of Dispersion

You are studying whether sentence length for weapons offenses, measured in months, is affected by the classification of the firearm used in the offense (categorized as handgun, rifle, shotgun, assault weapon, or Class III firearm). For a sample of 12 offenders convicted of weapons offenses in Washington, D.C., the length of prison terms in months were as follows: 6 6 2 12 36 48 60 24 24 20 18 15

What is the independent variable? The dependent variable? How is each variable measured?

1)IV:

2)DV:

What is the sample? The unit of observation? A reasonable population?

1)Sample:

2)Unit of Observation:

3)Population:

c.Calculate the mean, median and mode for these data.

d.Calculate the range for these data.

e.Calculate the interquartile range (IQR) for these data using the exact method.

f.Which is a better measure of dispersion and why?

Explanation / Answer

For a sample of 12 offenders convicted of weapons offenses in Washington, D.C., the length of prison terms in months were as follows: 6 6 2 12 36 48 60 24 24 20 18 15

1 )IV: Firearm used in the offence (type of firearm)

2) DV: Sentence length for weapon offence (in months)

What is the sample? The unit of observation? A reasonable population?

1) Sample: 12 offenders who are convicted of weapons offenses in Washington, D.C

2) Unit of Observation: the length of prison terms in months.

3) Population: Offenders who are convicted of weapons offenses in Washington, D.C

c.Calculate the mean, median and mode for these data.

Count = 12

Sum = 271

Mean = 22.583333333333

Median = 19

Mode = 6, 24

d.Calculate the range for these data.

Lowest value: 2
Highest value: 60

Range: 58

e.Calculate the interquartile range (IQR) for these data using the exact method.

Lower quartile (xL): 7.5
Upper quartile (xU): 33

Interquartile range (xU-xL): 25.5

f. Which is a better measure of dispersion and why?

One must decide which measure of dispersion best describes the spread in a set of data. The range is the crudest way to estimate the spread of the data values. However, it is easy to calculate because it relies on a very simple formula containing two data values, the highest one and the lowest one. The range is an adequate estimate for a data set of no more than five values. The standard deviation is a more reliable measure because it depends on all data values and is less susceptible to outliers. Its calculation is more involved than that of the range.

Thus, Standard deviation is a better measure of dispersion.

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