Question

The following table gives the robbery rate per 100,000 people for 26 states east of the Mississippi River, as compiled by the FBI in 2005:

117.3	20.9	111.5	32.4	85.6	12.5	161.9	191.3	139.1
200.6	107.4	117.9	156.5	86.6	142.9	194.9	156.9	245.8
146.7	140.6	95.4	36.5	132.9	74.8	116.9	162.4

a. Construct a frequency distribution table. Take the classes to as 10-50, 50-90, 90-130, 130-170, 170-210, and 210-250 (using the “less than” method”, e.g., 10 to less than 50, etc).

b. Calculate the relative frequencies for all classes.

c. Calculate the cumulative frequencies and relative cumulative frequencies for each class.

d. What percentage of these states have a robbery rate of at least 130 per 100,000 people?

e. Construct a histogram (bar graph) for the relative frequency distribution.

f. Draw an ogive (relative cumulative frequency curve) for this data.

Answer 1

Class Interval	Frequency
10-50	4
50-90	3
90-130	6
130-170	9
170-210	3
210-250	1
Sum	26

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Relative frequency = Frequency / Sum of frequency

b)

Class Interval	Frequency	Relative Fre
10-50		0.1538
50-90		0.1154
90-130		0.2308
130-170		0.3462
170-210		0.1154
210-250		0.0385
Total		1.0000

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c)  

Class Interval	Frequency	Relative Fre	Cumulative frequency	Cumulative relatative frequency
10-50	4	0.1538	4	0.1538
50-90	3	0.1154	7	0.2692
90-130	6	0.2308	13	0.5000
130-170	9	0.3462	22	0.8462
170-210	3	0.1154	25	0.9615
210-250	1	0.0385	26	1.0000
Total	26	1.0000

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d)

Class Interval	Frequency	Relative Fre	Cumulative relatative frequency	%Cumutaltive relative frequency
10-50	4	0.1538	0.1538	15.38
50-90	3	0.1154	0.2692	26.92
90-130	6	0.2308	0.5000	50.00
130-170	9	0.3462	0.8462	84.62
170-210	3	0.1154	0.9615	96.15
210-250	1	0.0385	1.0000	100
Total	26	1.0000

P(x>=130) =(9+3+1)/26= 50%

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e)

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f)