CA Foundation P3 · Chapter 13

Statistical Description of Data and Sampling MCQs with Answers

9 multiple-choice questions on Statistical Description of Data and Sampling for CA Foundation P3 Quantitative Aptitude. Try each one before revealing the answer and explanation.

1. Question 1

   Data collected by an investigator directly from the source for a specific purpose are called:

   • A) Primary data
   • B) Secondary data
   • C) Discrete data
   • D) Qualitative data
   Show answer & explanation

   Answer: A) Primary data

   Primary data are original data collected first-hand by the investigator for the enquiry at hand. Secondary data are data already collected by someone else and used again.

2. Question 2

   In a frequency distribution with inclusive classes 10–19, 20–29, 30–39, the class boundaries of the class 20–29 are:

   • A) 20 – 29
   • B) 19 – 30
   • C) 20 – 30
   • D) 19.5 – 29.5
   Show answer & explanation

   Answer: D) 19.5 – 29.5

   The gap between consecutive inclusive classes is 1 (e.g. 19 and 20). Half the gap, 0.5, is subtracted from the lower limit and added to the upper limit. So the boundaries are 20 − 0.5 = 19.5 and 29 + 0.5 = 29.5.

3. Question 3

   Which of the following graphs is used to locate the median of a frequency distribution graphically?

   • A) Histogram
   • B) Frequency polygon
   • C) Ogive
   • D) Pie chart
   Show answer & explanation

   Answer: C) Ogive

   The median is read from the ogive (cumulative frequency curve) at the point corresponding to N/2, or at the intersection of the less-than and more-than ogives. A histogram is used to locate the mode graphically.

4. Question 4

   In a family budget of ₹18,000 per month, the expenditure on food is ₹4,500. In a pie chart of the budget, the angle of the food sector is:

   • A) 25°
   • B) 45°
   • C) 90°
   • D) 120°
   Show answer & explanation

   Answer: C) 90°

   Angle = (component / total) x 360° = (4,500/18,000) x 360° = 0.25 x 360° = 90°. The value 25° confuses the 25% share with degrees.

5. Question 5

   The frequencies of five consecutive classes are 5, 8, 12, 15 and 10. The 'less than' cumulative frequency of the third class is:

   • A) 12
   • B) 20
   • C) 35
   • D) 25
   Show answer & explanation

   Answer: D) 25

   The less-than cumulative frequency adds frequencies up to and including the class: 5 + 8 + 12 = 25. 12 is only the frequency of the third class.

6. Question 6

   The number of possible samples of size 3 that can be drawn without replacement from a population of 10 units (order not considered) is:

   • A) 120
   • B) 1000
   • C) 720
   • D) 30
   Show answer & explanation

   Answer: A) 120

   Without replacement and ignoring order, the number of samples is ¹⁰C₃ = 10 x 9 x 8 / 6 = 120. With replacement and order considered it would be 10³ = 1,000, and ¹⁰P₃ = 720 counts ordered samples.

7. Question 7

   A sampling method in which the population is divided into homogeneous sub-groups and a random sample is drawn from each sub-group is called:

   • A) Cluster sampling
   • B) Stratified sampling
   • C) Systematic sampling
   • D) Purposive sampling
   Show answer & explanation

   Answer: B) Stratified sampling

   In stratified sampling the population is split into homogeneous strata and units are drawn randomly from every stratum. In cluster sampling whole clusters (which are internally heterogeneous) are selected.

8. Question 8

   A population has a standard deviation of 12. The standard error of the sample mean for a random sample of size 36 (drawn with replacement) is:

   • A) 1/3
   • B) 2
   • C) 6
   • D) 4
   Show answer & explanation

   Answer: B) 2

   Standard error of the mean = σ/√n = 12/√36 = 12/6 = 2. Dividing by n instead of √n gives 12/36 = 1/3, and 6 is merely √36 (the divisor itself), not the standard error.

9. Question 9

   A systematic sample of 30 units is drawn from a numbered population of 600 units. If the first unit selected is number 7, the 12th unit selected is:

   • A) 247
   • B) 220
   • C) 207
   • D) 227
   Show answer & explanation

   Answer: D) 227

   Sampling interval k = N/n = 600/30 = 20. The r-th unit selected is 7 + (r − 1) x 20. For r = 12: 7 + 11 x 20 = 227. Using 12 x 20 gives 247, which is the 13th unit.