ICAP PRC-2 Application of statistics in business: practice questions with answers

Question 1

Rehman Pharma wants the views of chemist shops in Punjab on a new delivery schedule. It lists the 120 towns where it has customers, selects 8 of those towns at random and then surveys every chemist shop in the 8 selected towns. Which sampling method is Rehman Pharma using?

1. A Stratified random sampling
2. B Cluster sampling
3. C Quota sampling
4. D Systematic sampling

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Answer: B. The population (chemist shops) falls into natural groups (towns). Choosing some groups at random and examining all members of each chosen group is cluster sampling. It is cheap because fieldwork is concentrated in 8 towns, but the sample may be less representative than a stratified sample if shops in different towns differ.

Question 2

The sales director of an Islamabad software house wants one chart that shows, for each of the last four years, both total sales and how that total was split between its three service lines (apps, cloud hosting and support), so that the years can be compared side by side. Which chart is most suitable?

1. A A component (sectional) bar chart
2. B A single pie chart of the four years' sales
3. C A histogram of sales by year
4. D An ogive (cumulative frequency curve)

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Answer: A. A component (sectional) bar chart draws one bar per year whose height is total sales, divided into sections for apps, cloud hosting and support. It shows both the change in the total and the make-up of each year's total. (A percentage component bar chart would show only the shares; a multiple bar chart would show the parts side by side but not the total as a single bar.)

Question 3

For the monthly salaries of staff at a Sukkur rice mill, the lower quartile is Rs 28,000 and the upper quartile is Rs 46,000. What is the quartile deviation (semi-interquartile range)?

1. A Rs 18,000
2. B Rs 37,000
3. C Rs 9,000
4. D Rs 4,500

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Answer: C. Quartile deviation = (Q3 − Q1) / 2 = (46,000 − 28,000) / 2 = 18,000 / 2 = Rs 9,000. It measures the spread of the middle 50% of salaries and, unlike the range, is not affected by extreme values.

Question 4

A building-materials price index for Islamabad (2018 = 100) stood at 148 in 2022 and 185 in 2025. The index is to be rebased so that 2022 = 100. Which statement is correct?

1. A 2025 index 125.00; prices rose 25% from 2022 to 2025
2. B 2025 index 137.00; prices rose 37% from 2022 to 2025
3. C 2025 index 125.00; prices rose 37% from 2022 to 2025
4. D 2025 index 80.00; prices fell 20% from 2022 to 2025

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Answer: A. To rebase, divide every value by the value of the new base year and multiply by 100:

- 2025 (2022 = 100) = 185 / 148 × 100 = 125.00
- The change from 2022 to 2025 is 37 index points but a 25% rise in prices.

Question 5

Between 2023 and 2025 the average money wage of workers at a Hattar packaging plant rose by 30%, while a local consumer price index rose by 40%. What happened to the workers' real wages over the period?

1. A Real wages fell by 10.00%
2. B Real wages fell by 7.14%
3. C Real wages fell by 7.69%
4. D Real wages rose by 30.00%

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Answer: B. Real wage index = money wage index / price index × 100 = 130 / 140 × 100 = 92.86.

Change in real wages = 92.86 − 100 = −7.14%: workers can buy about 7% less than in 2023, despite the 30% pay rise.

Question 6

An analyst at a Karachi bank finds a correlation of 0.91 over 24 months between the number of air conditioners sold in the city and the bank's own monthly electricity bill. She proposes a regression of the bill on air-conditioner sales to budget electricity costs. What is the main weakness of this approach?

1. A A correlation of 0.91 is too weak for any regression line to be useful
2. B A regression line cannot be fitted unless x is proven to cause changes in y
3. C Both series probably rise with hot weather, so the link is only indirect
4. D The correlation should be negative, as bank usage falls when sales rise

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Answer: C. Correlation and regression measure association, not causation. Both series rise in hot months, so the strong r reflects a third factor (temperature) rather than any direct link between the city's air-conditioner sales and the bank's bill. A forecast built on such a spurious relationship can fail as soon as the link changes (a cool summer with a sales promotion, or new energy-saving equipment at the bank). A better explanatory variable would be temperature or the bank's own usage drivers.