In: Statistics and Probability
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]
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 |