# mode and median

Module 2 Assignment
Chapter 4
1. The following frequency distribution contains information about urban residents’ self-evaluation of the likelihood that they will be a victim of crime in the next year.

Likelihood of
Victimization Urban
Very Likely 90
Somewhat Likely 70
Not Likely 80
Total 240

a) Find the mode
b) Find the median
c) Why would you not want to report the mean for this variable?

2. The following frequency distribution contains information on reading level of 32 inmates.

Reading level for 32 inmates
1 1
2 0
3 3
4 1
5 1
6 3
7 4
8 10
9 3
10 4
11 1
12 1
32

a) Calculate Percentage of inmates at each grade level
b) Calculate the cumulative percentage
c) Find the mode
d) Find the median
e) Find the mean
f) What is the 25th percentile?
g) What is the 75th percentile?

3. You listen to a political debate between two politicians. One claims that the average income of all American workers is \$74,802; the others say that American workers, on average make only \$62,149. Is it possible for both these politicians to be correct? If so, explain how.
Chapter 5
4. Imagine now that in addition to the information we gathered on urban residents in Question 1 above, we also collected data on Non-urban residents and their self-evaluation of the likelihood of victimization.

Likelihood of Victimization Urban Not Urban Total
Very Likely 90 10 100
Somewhat Likely 70 230 300
Not Likely 80 320 400
Total 240 560 800

5. In a national survey, psychological distress was measured on a scale between 0 and 24. In the Table below you will see separate data on two groups of respondents’ distress scores; those who had been a victim of a violent crime and those who have not.

Psychological Distress Victim Not Victim
Mean 4.9 3.5
Y 916 7000
Y-Mean Y)2 6059.14 20180.2
N 187 2000

Variance 32.4018182 10.0901
SD 5.6922595 3.17649178

a) Calculate the variance and standard deviation from these statistics for both groups. Hint: a lot of the work has been done for you.)
b) What can you say about the variability in the distress scores for those who have been victimized compared to those who have not?
c) Why might there be a difference? Why might there be more variability for one group rather than the other?
Module 2 Learning Check
Why can we NOT assume that for any interval-ratio variable, 50% of cases are above the mean and 50% are below the mean? Give an example from criminology or criminal justice other than those given in the text or lecture.

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