Level 1
Statistics MCQs set 3 for Punjab Police Sub Inspector (BS-14) Mathematics — 20 solved questions.
Q1. In a frequency distribution, the class with the highest frequency is called the:
Answer: Modal class
Explanation: In a frequency distribution the class with the highest frequency is called the modal class, because its value corresponds to the mode.
Q2. The mean of 8, 8, 8, 8, 8 is:
Answer: 8
Explanation: The mean is the sum divided by the count: (8+8+8+8+8)/5 = 40/5 = 8.
Q3. Standard deviation is the square root of:
Answer: Variance
Explanation: Variance measures the average squared deviation from the mean; standard deviation is defined as the positive square root of variance.
Q4. The IQR (Interquartile Range) is calculated as:
Answer: Q3 minus Q1
Explanation: The interquartile range measures the spread of the middle 50% of data, calculated as the third quartile minus the first quartile.
Q5. A histogram is used to display:
Answer: Frequency distribution of continuous data
Explanation: A histogram uses adjacent bars to display the frequency distribution of continuous (or grouped) quantitative data.
Q6. The value that appears most often in a data set is called:
Answer: Mode
Explanation: By definition, the mode is the value that occurs most frequently in a data set.
Q7. The mean of 6 numbers is 12. If one number is removed and the new mean becomes 11, what was the removed number? (Sum was 72, new sum 55, removed = 72-55 = 17)
Answer: 17
Explanation: Original sum = 6 × 12 = 72; after removing one number, new sum = 5 × 11 = 55; so the removed number = 72 − 55 = 17.
Q8. Find the median of: 14, 3, 27, 8, 19, 22. Sorted: 3, 8, 14, 19, 22, 27. Median = (14+19)/2 = 16.5
Answer: 16.5
Explanation: Sorting the six values gives 3,8,14,19,22,27; the median of an even set is the mean of the two middle values: (14+19)/2 = 16.5.
Q9. For the data 2, 4, 4, 6, 8, the variance is: Mean=4.8 (sum=24/5). Deviations: -2.8,-0.8,-0.8,1.2,3.2. Squared: 7.84,0.64,0.64,1.44,10.24. Variance = 20.8/5 = 4.16
Answer: 4.16
Explanation: With mean = 4.8, the squared deviations are 7.84, 0.64, 0.64, 1.44, and 10.24; their average is 20.8/5 = 4.16.
Q10. The geometric mean of 4 and 16 is:
Answer: 8
Explanation: Geometric mean of two numbers a and b = √(a×b) = √(4×16) = √64 = 8.
Q11. For the data set 5, 10, 15, 20, 25, 30, 35, 40 the Q1 (25th percentile) value is the average of 2nd and 3rd values: (10+15)/2 = 12.5
Answer: 12.5
Explanation: For 8 values, Q1 is the average of the 2nd and 3rd values: (10+15)/2=12.5.
Q12. The standard deviation of 2, 4, 4, 4, 5, 5, 7, 9 is: Mean=5, deviations squared sum=32, variance=4, SD=2
Answer: 2
Explanation: With mean = 5 and sum of squared deviations = 32 over 8 values, variance = 32/8 = 4, so standard deviation = √4 = 2.
Q13. In a frequency distribution, the class midpoint is calculated as:
Answer: (Upper limit plus lower limit) divided by 2
Explanation: A class midpoint splits the class interval evenly and is calculated as (upper class limit + lower class limit) ÷ 2.
Q14. The harmonic mean of 2 and 8 is: HM = 2/(1/2 + 1/8) = 2/(4/8 + 1/8) = 2/(5/8) = 16/5 = 3.2
Answer: 3.2
Explanation: The harmonic mean of two numbers a and b is 2ab/(a+b); for 2 and 8: 2×2×8/(2+8)=32/10=3.2.
Q15. In a bar chart showing monthly sales, the height of each bar represents:
Answer: The frequency or value for that category
Explanation: In a bar chart, the height (or length) of each bar is proportional to the frequency or value it represents for that category.
Q16. If Q1 = 20 and Q3 = 50, the interquartile range (IQR) is:
Answer: 30
Explanation: The interquartile range is Q3 minus Q1: 50 − 20 = 30, measuring the spread of the middle 50% of data.
Q17. Which chart is best for showing parts of a whole as percentages?
Answer: Pie chart
Explanation: A pie chart divides a circle into sectors whose sizes are proportional to each category's percentage share of the whole.
Q18. The mean of 10 values is 25. Six of those values have a mean of 20. What is the mean of the remaining 4 values? Total sum=250, sum of 6=120, sum of 4=130, mean=130/4=32.5
Answer: 32.5
Explanation: Total sum = 10×25 = 250; sum of 6 values = 6×20 = 120; remaining sum = 130; mean of 4 = 130/4 = 32.5.
Q19. The data set is 10, 20, 30, 40, 50. The coefficient of variation (CV = SD/Mean x 100) is: Mean=30, Variance=200, SD=√200=14.14, CV=14.14/30 x 100 = 47.14%
Answer: 47.14%
Explanation: Mean=30, variance=[(10-30)²+(20-30)²+(30-30)²+(40-30)²+(50-30)²]/5=200, SD=√200≈14.14, CV=14.14/30×100≈47.14%. 47.14% is correct because it matches what the question requires. Show the calculation clearly when solving similar quantitative items.
Q20. For data 1, 3, 5, 7, 9, 11, 13, what is the interquartile range? Q1=3, Q3=11, IQR=11-3=8
Answer: 8
Explanation: For the ordered data 1,3,5,7,9,11,13: Q1 = 3 and Q3 = 11, so IQR = Q3−Q1 = 11−3 = 8.