Question

In: Statistics and Probability

QUESTION ONE a) Define the following: i. Statistics [2 Marks] ii. Probability [2 Marks] b) Road...

QUESTION ONE
a) Define the following:
i. Statistics [2 Marks]
ii. Probability [2 Marks]
b) Road Safety said that it would commence the enforcement of Safety Laws from
Wednesday, 11th July 2018 as part of the Road Safety
Management System. The Head of Public Relations, said
that the programme would include the introduction of
roadside cameras to monitor and detect traffic offences. The
following is a frequency distribution of speeds for a sample of
475 vehicles which were scanned by one of the cameras on Great East Road on
a public holiday.

Speed

45 – 49

50 – 54

55 – 59

60 – 64

65 – 69

70 – 74

75 – 79

Frequency

10

40

150

175

75

15

10

Compute the following statistics for the scanned vehicles:
i. Mean speed. [2 marks]
ii. Modal speed. [4 marks]
iii. Median speed [4 marks]
iv. Standard deviation [4 marks]
v. Coefficient of variation. [2 mark]
[TOTAL: 20 MARKS]

Solutions

Expert Solution

a.

i. Statistics: Statistics is used as a plural noun and also as a singular noun.

In plural sense, numerical data, i.e., numerical statements of facts in connection with any field of human experience are called statistics. For example, production statistics of a factory over different years, statistics of birth and death of a country, etc.

The term statistics, in singular sense, means the aggregate of scientific methods which deals with the collection, presentation, analysis and interpretation of numerical data. This singular sense of statistics is used in the statement, "R. A. Fisher had contributed a lot in various branches of statistics.".

ii. Probability: Suppose the total no. of elementary events in a sample space is n, where n is finite and the elementary events are equally likely, and n(E) of them are favourable to an event E. Then probability of event E, denoted by P(E), is defined as

P(E)=n(E)/n. This is a classical definition of probability.

b.

Speed Class boundary Frequency (f) Mid value (x) Cumulative frequency (< type) xf x^2f
45-49 44.5-49.5 10 47 10 470 22090
50-54 49.5-54.5 40 52 50 2080 108160
55-59 54.5-59.5 150 57 200 8550 487350
60-64 59.5-64.5 175 62 375 10850 672700
65-69 64.5-69.5 75 67 450 5025 336675
70-74 69.5-74.5 15 72 465 1080 77760
75-79 74.5-79.5 10 77 475 770 59290
Total= 28825 1764025


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