Question

In a study of parole board decision making in a Midwestern state, offenders were measured on the number of previous incarcerations. The data is presented below.

a) Calculate the mode, median and mean. b) What is the shape of this distribution? c) What explains the distribution’s shape?

Prior Incarcerations (x)	Frequency (f)
6	1
5	2
4	3
3	15
2	35
1	85
0	312

Answer 1

(a)

(i)

Maximum Frequency = f = 312.

Corresponding variable value = x = 0

So,

Mode = 0

(ii)

Cumulative Distribution is got as follows:

x	Cumulative Frequency
6	1
5	3
4	6
3	21
2	56
1	141
0	453

Total Frequency = N = 453

So,

N/2 = 453/2 = 226.5

Median is Size of N/2th item

= Size of 226.5th item

Here 226.5 is reached at 453 and the corresponding variate value is 0.

So,

Median = 0

(iii)

x	f	x f
6	1	6
5	2	10
4	3	12
3	15	45
2	35	70
1	85	85
0	312	0
Total =	453	228

Mean = 228/453

= 0.5033

(b)

The shape of this distribution : Positively Skewed

(c)

Mean = 0.5033 is greater than Median = 0 explains the distribution’s shape, because for Positively Skewed Distribution Mean is greater than Median.