Question

Driving under the influence of alcohol (DUI) is a serious offense. The following data give the ages of a random sample of 50 drivers arrested while driving under the influence of alcohol. This distribution is based on the age distribution of DUI arrests given in the Statistical Abstract of the United States46 16 41 26 22 33 30 22 36 3463 21 26 18 27 24 31 38 26 5531 47 27 43 35 22 64 40 58 2049 37 53 25 29 32 23 49 39 4024 56 30 51 21 45 27 34 47 35(b) Make a frequency table using seven classes.Class Limits... Class Boundaries...Midpoint...Frequency...RelativeFrequency...CumulativeFrequency

Answer 1

Explanation below.

Explanation:

For this case we have the following dataset:

46, 16, 41, 26, 22 ,33, 30, 22 ,36, 34,

63, 21, 26, 18, 27, 24, 31, 38, 26, 55,

31, 47, 27, 43 ,35, 22 ,64,40, 58, 20,

49, 37, 53, 25, 29, 32, 23, 49, 39, 40,

24, 56, 30, 51, 21, 45, 27, 34, 47, 35

So we have 50 values. The first step on this case would be order the dataset on increasing way and we got:

16, 18, 20, 21, 21, 22, 22, 22, 23, 24,

24, 25, 26, 26, 26, 27, 27, 27, 29, 30

30, 31, 31, 32, 33, 34, 34, 35, 35, 36,

37, 38, 39, 40, 40, 41, 43, 45, 46, 47,

47, 49, 49, 51, 53, 55, 56, 58, 63, 64

We can find the range for this dataset like this:

`Range = Max-Min = 64-16 =48`

Then since we need 7 classes we can find the length for each class doing this:

`W = (48)/(7)=6.86`

And now we can define the classes like this and counting how many observations lies on each interval we got the frequency:

Class Frequency Midpoint RF CF

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[16-22.86) 8 19.43 (8/50)=0.16 0.16

[22.86-29.71) 11 26.29 (11/50)=0.22 0.38

[29.71-36.57) 11 33.14 (11/50)=0.22 0.6

[36.57-43.43) 7 40.0 (7/50)=0.14 0.74

[43.43-50.29) 6 46.86 (6/50)=0.12 0.86

[50.29-57.14) 4 53.72 (4/50)=0.08 0.94

[57.14-64] 3 60.57 (3/50)=0.06 1.0

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Total 50 1.00

RF= Relative frequency. CF= Cumulative frequency

The relative frequency was calculated as the individual frequency for a class divided by the total of observations (50)

The mid point is the average between the limits of the class.

And the cumulative frequency is calculated adding the relative frequencies for each class.