Question

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Solve the following questions

Q1

1. Construct a cumulative frequency distribution of the 20 brain volumes(cm³) listed below.

Use the classes 900-999, 1000-1099, and so on. (6-classes)

1005   963 1035 1027 1281 1272 1051 1079 1034 1070 1173 1079 1067 1104 1347 1439 1029 1100 1204 1160.Also find relative frequency for each class interval?

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Q2

1. Use data above in question 1 to build the frequency polygon. Is the distribution symmetric?

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Q3

1. Find the mean, mode, median, variance, Standard Deviation, and range of the following data:

1	4	2
2	5	1
3	6	3
4	7	4
5	8	1

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Q4

1. Find the mean and the Variance of the following sample data:

           

x	Frequency (f)
1	5
2	6
4	9
8	6
12	4

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Q5

1. Two dice with six faces are rolled, find the sample space and number of elements in the sample space. Also calculate the probability that the sum of the two faces is equal 6.

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Q6

1. Use the Prison and Plea data in following table to calculate part a and b :

	Guilty Plea	Plea of not Guilty
Sentenced to Prison	392	58
Not Sentenced to Prison	564	14

1. If someone from the 1028 subjects is randomly selected, find the probability of selecting someone sentenced to prison.
2. If someone from the 1028 subjects is randomly selected, find the probability of selecting someone sentenced to prison and entered a Guilty Plea.

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Answer 1

Q1

Class limits	Frequency (f)	Cumulative Frequency	Relative frequency
900-999	1	1	0.05
1000-1099	10	11	0.5
1100-1199	4	15	0.2
1200-1299	3	18	0.15
1300-1399	1	19	0.05
1400-1499	1	20	0.05
Total	20		1

Q2

Yes, the distribution seems symmetric as the curve is bell shaped.

Q3

Mode is the value which occurs most frequently

Here, value '1' and value '4' appears 3 times each

So, Mode = 1, 4

Range = Maximum value - Minimum value

Maximum value = 8

Minimum value = 1

Range = Maximum value - Minimum value = 8 - 1 = 7

Q4

Q5

Sample Space :

Number of elements in the sample space = 6² = 36

Probability that the sum of the two faces is equal 6 = Number cases when sum of the two faces is equal 6 / Total cases

Cases when sum of the two faces is equal 6 : ( 1,5 ) , ( 2,4 ) , ( 3,3 ) , ( 4,2 ) , ( 5,1 )

So, Number cases when sum of the two faces is equal 6 = 5

Total cases = 36

Probability that the sum of the two faces is equal 6 = 5 / 36 = 0.139

Q6

We have the table as :

	Guilty Plea	Plea of not Guilty	Total
Sentenced to Prison	392	58	450
Not Sentenced to Prison	564	14	578
Total	956	72	1028

a.

Probability of selecting someone sentenced to prison = Number of people sentenced to prison / Total people

= 450 / 1028 = 0.438

b.

Probability of selecting someone sentenced to prison and entered a Guilty Plea

= Number of people sentenced to prison and entered a Guilty Plea / Total people

= 392 / 1028 = 0.381