CIMA BA1 · Chapter 9
Summarising and analysing data MCQs with Answers
11 multiple-choice questions on Summarising and analysing data for CIMA BA1 Fundamentals of Business Economics. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
Primary data are best described as:
- A) Data originally collected for another purpose, such as published government statistics
- B) Data that have already been summarised into averages
- C) Data collected specifically for the purpose of the current investigation
- D) Data relating only to the main products of a business
Show answer & explanation
Answer: C) Data collected specifically for the purpose of the current investigation
Primary data are collected first-hand for the specific investigation, for example through a survey designed for the purpose. Secondary data were collected for some other purpose and are reused, such as official statistics or trade publications.
Question 2
The weekly number of complaints received by a customer service team over seven weeks was: 12, 15, 9, 20, 15, 18, 11. What is the arithmetic mean number of complaints per week (to two decimal places)?
- A) 15.00
- B) 14.29
- C) 16.67
- D) 11.00
Show answer & explanation
Answer: B) 14.29
Mean = sum of values / number of values = (12 + 15 + 9 + 20 + 15 + 18 + 11) / 7 = 100 / 7 = 14.29. The median and mode are both 15 and the range is 20 - 9 = 11.
Question 3
Order sizes have been grouped as follows: 0 to under 10 units: 4 orders 10 to under 20 units: 10 orders 20 to under 30 units: 6 orders Using class midpoints, what is the estimated mean order size?
- A) 16.0 units
- B) 21.0 units
- C) 11.0 units
- D) 15.0 units
Show answer & explanation
Answer: A) 16.0 units
Midpoints are 5, 15 and 25. Sum of fx = 5 x 4 + 15 x 10 + 25 x 6 = 20 + 150 + 150 = 320. Total frequency = 20. Mean = 320 / 20 = 16.0 units.
Question 4
Treating the values 2, 4, 6, 8 and 10 as a complete population, what is their standard deviation (to two decimal places)?
- A) 8.00
- B) 3.16
- C) 2.40
- D) 2.83
Show answer & explanation
Answer: D) 2.83
Mean = 30 / 5 = 6. Squared deviations: 16, 4, 0, 4, 16, totalling 40. Variance = 40 / 5 = 8. Standard deviation = square root of 8 = 2.83. Dividing by n - 1 instead would give 3.16.
Question 5
A set of data has a mean of 40 and a standard deviation of 6. What is the coefficient of variation?
- A) 667%
- B) 90%
- C) 15%
- D) 6%
Show answer & explanation
Answer: C) 15%
Coefficient of variation = standard deviation / mean x 100% = 6 / 40 x 100% = 15%. It is a relative measure of dispersion, useful for comparing the variability of data sets with different means.
Question 6
For a distribution that is positively skewed, which of the following relationships between the averages is usually expected?
- A) Mode > median > mean
- B) Mean > median > mode
- C) Mean = median = mode
- D) Median > mean > mode
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Answer: B) Mean > median > mode
In a positively skewed distribution the tail extends to the right, with a few high values pulling the mean upwards. The mode is at the peak, the median lies between, and the mean is highest. In a symmetrical distribution all three are equal.
Question 7
Big data is commonly described by reference to which of the following characteristics?
- A) Volume, velocity and variety
- B) Validity, valuation and verification
- C) Volume, viability and vision
- D) Velocity, verification and vertical integration
Show answer & explanation
Answer: A) Volume, velocity and variety
Big data refers to data sets that are very large (volume), generated and processed at high speed (velocity) and in many formats, including unstructured data such as text, images and sensor readings (variety). Veracity and value are sometimes added as further characteristics.
Question 8
A researcher divides a population of customers into groups by region and then selects a random sample from each region in proportion to its size. This sampling method is:
- A) Cluster sampling
- B) Quota sampling
- C) Systematic sampling
- D) Stratified random sampling
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Answer: D) Stratified random sampling
Stratified sampling divides the population into strata with a shared characteristic and takes a random sample from each, usually in proportion to the stratum size. Quota sampling is non-random selection within groups, cluster sampling selects whole groups, and systematic sampling picks every nth item from a list.
Question 9
The lower quartile of a distribution is 24 and the upper quartile is 40. What is the quartile deviation (semi-interquartile range)?
- A) 16
- B) 32
- C) 8
- D) 64
Show answer & explanation
Answer: C) 8
Interquartile range = Q3 - Q1 = 40 - 24 = 16. Quartile deviation = interquartile range / 2 = 16 / 2 = 8.
Question 10
Branch A has 20 employees with a mean weekly wage of $600. Branch B has 30 employees with a mean weekly wage of $700. What is the mean weekly wage for all employees of both branches?
- A) $650
- B) $660
- C) $640
- D) $1,300
Show answer & explanation
Answer: B) $660
The combined mean must be weighted by the number of employees. Total wages = 20 x 600 + 30 x 700 = 12,000 + 21,000 = 33,000. Combined mean = 33,000 / 50 = $660.
Question 11
The number of faulty items found in each of 30 batches inspected was: 0 faulty items: 6 batches 1 faulty item: 9 batches 2 faulty items: 10 batches 3 faulty items: 3 batches 4 faulty items: 2 batches Treating the 30 batches as the whole population, what is the standard deviation of the number of faulty items per batch (to two decimal places)?
- A) 1.12
- B) 1.25
- C) 1.90
- D) 1.41
Show answer & explanation
Answer: A) 1.12
Sum of f = 30. Sum of fx = 0 + 9 + 20 + 9 + 8 = 46, so mean = 46 / 30 = 1.5333. Sum of fx squared = 0 + 9 + 40 + 27 + 32 = 108, so sum of fx squared / sum of f = 3.6. Variance = 3.6 - 1.5333 squared = 3.6 - 2.3511 = 1.2489. Standard deviation = square root of 1.2489 = 1.12 (rounded to two decimal places). 1.25 is the variance, 1.90 is the square root of 3.6 (forgetting to subtract the squared mean) and 1.41 ignores the frequencies.