Question

You are studying the impact of the number of prior arrests on sentence length, in months, for a sample of 94 criminal defendants from the Prince George’s County District Court.  The following frequency distribution represents the number of prior arrests for your sample of 94 defendants.   Note that, this assignment requires that you calculate the cumulative frequency, percentage, cumulative percentage, etc….etc.

Prior Arrests         f
0                          20
1                          16
2                           8
4                          10
5                           9
6                           5
10                          7
11                          6
15                          5
20                          4
25                          4

1. Calculate the mean, median, and mode.  Which measure of central tendency is most appropriate for this data (explain why)?

    b).Calculate the standard deviation and variance. Interpret the standard deviation.

Answer 1

a)

x	f	x*f	x*f^2
0	20	0	0
1	16	16	16
2	8	16	32
4	10	40	160
5	9	45	225
6	5	30	180
10	7	70	700
11	6	66	726
15	5	75	1125
20	4	80	1600
25	4	100	2500
Total	94	538	7264

mean =xf/ f =538/94 =5.723

median =(n+1)/2 th value =(94+1)/2 th value =47.5 th value =4

mode =0 (as it appears with maximum frequency)

as distribution is right skewed therefore most appropriate measure of central tendency is median

b)

variance =(fx²-(fx)²/n))/(n-1)=(7264-538²/94)/93 =44.9979

std deviation =sqrt(44.9979)=6.7081

std deviation is average distance of a random variable from true population value