Question

2. a) The distribution of marks obtained by 500 candidates in a particular exam is given
below:

Marks more than: 0 10 20 30 40 50
Number of candidates 500 460 400 200 100 30

Calculate the lower quartile marks. If 70% of the candidates pass in the exam, find
the minimum marks obtained by a pass candidate. (5)
b) An analysis of monthly wages paid to the workers of two firms A and B belonging
to the same industry gives the following results:

Firm A Firm B
Number of workers 500 600
Average daily wages ` 186 ` 175
Variance of distribution of wages 81 100

i) Which firm, A or B, has a large wage bill?
ii) In which firm, A or B, is there greater variability in individual wages

Answer 1

Answer on Question #60594 – Math – Statistics and Probability

Question

2. a) The distribution of marks obtained by 500 candidates in a particular exam is given below:

Marks more than: 0 10 20 30 40 50

Number of candidates 500 460 400 200 100 30

Calculate the lower quartile marks. If 70% of the candidates pass in the exam, find the minimum marks obtained by a pass candidate.

Solution

The lower quartile marks are between 20 and 30.

If 70% of the candidates pass in the exam, then only 30% don't pass it.

The minimum marks obtained by a pass candidate are between 20 and 30.

Question

b) An analysis of monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following results:

i) Which firm, A or B, has a large wage bill?

ii) In which firm, A or B, is there greater variability in individual wages

Solution

i) Firm A

Total monthly wage = $186 · 500 = $93000.

Firm B

Total monthly wage = $175 · 600 = $105000.

Firm B pays out larger amount of monthly wage.

ii)

Firm A

Coefficient of variation = $\frac{\sigma}{\bar{x}} = \frac{\sqrt{81}}{186} = 0.0484$.

Firm B

Coefficient of variation = $\frac{\sigma}{\bar{x}} = \frac{\sqrt{100}}{175} = 0.0571$.

There is greater variability in wages in Firm B.

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