Question

In: Statistics and Probability

The number of crimes reported (in millions) and the number of arrests reported (in millions) by...

The number of crimes reported (in millions) and the number of arrests reported (in millions) by the U.S. Department of Justice for 14 years is listed below.

Crimes 1.66 1.65 1.60 1.55 1.44 1.40 1.32 1.23 1.22 1.23 1.22 1.18 1.16 1.19

Arrests 0.72 0.72 0.78 0.80 0.73 0.72 0.68 0.64 0.63 0.63 0.62 0.60 059 0.60

1. Find the Mean, Median, Mode, and Mid-range for both distributions of data.

2. Find the range, standard deviation, and variance for both distributions of data.

3. Create a box and whisker plot for both distributions of data. Please include the 5-Number Summary and identify any outliers appropriately.


Solutions

Expert Solution

1:

For data set Crimes:

Following table shows the ordered data set and total of data values:

S.No. Crimes
1 1.16
2 1.18
3 1.19
4 1.22
5 1.22
6 1.23
7 1.23
8 1.32
9 1.4
10 1.44
11 1.55
12 1.6
13 1.65
14 1.66
Total 19.05

The mean is

The median is: There are 14 data values so median will be average of 7th and 8th data values. That is median is

Mode: Mode is the data value with highest frequency. There are two data values with highest frequency 1.22 and 1.23. That is mode of the data sets are 1.22 and 1.23.

Mid range:

For data set Arrests:

Following table shows the ordered data set and total of data values:

S.No. Arrests
1 0.59
2 0.6
3 0.6
4 0.62
5 0.63
6 0.63
7 0.64
8 0.68
9 0.72
10 0.72
11 0.72
12 0.73
13 0.78
14 0.8
Total 9.46

The mean is

The median is: There are 14 data values so median will be average of 7th and 8th data values. That is median is

Mode: Mode is the data value with highest frequency. There are two data values with highest frequency 0.72. That is mode of the data set is 0.72.

Mid range:


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