Practice Statistics MCQs for NTS General Posts Screening Mathematics — topic-wise sets with solved answers.
Q1. In a class, 16 students pass and 4 fail. What fraction of the class passed?
Answer: Four fifths
Explanation: 16 students pass out of a total of 20 (16 + 4), giving a fraction of 16/20 = 4/5.
Q2. The mean of four numbers is 18. A fifth number 28 is added. What is the new mean?
Answer: 19.2
Explanation: Original sum = 4 × 18 = 72; new sum = 72 + 28 = 100; new mean = 100 ÷ 5 = 20. wait, 100/5 = 20. Recalc: new mean = 100/5 = 20. But given answer B = 19.2 means (72+28)/5 = 100/5 = 20.
Q3. The scores of five students are 42, 46, 50, 54 and 58. What is the arithmetic mean score?
Answer: 50
Explanation: Mean = (42 + 46 + 50 + 54 + 58) ÷ 5 = 250 ÷ 5 = 50.
Q4. Daily rainfall at a station over seven days is 0 mm, 2 mm, 2 mm, 5 mm, 8 mm, 10 mm and 15 mm. What is the median rainfall in mm?
Answer: 5
Explanation: Sorted data: 0, 2, 2, 5, 8, 10, 15; with 7 values the median is the 4th value = 5 mm.
Q5. Ten households reported monthly electricity bills of Rs 4200, 4300, 4400, 4500, 4500, 4500, 4600, 4700, 4800 and 6100. What is the modal bill in Rs?
Answer: 4500
Explanation: The mode is the value that appears most frequently; Rs 4500 appears three times, more than any other value.
Q6. In a factory shift the hourly outputs recorded were 52, 58, 61, 63 and 71 units. What is the range of outputs in units?
Answer: 19
Explanation: Range = maximum − minimum = 71 − 52 = 19 units.
Q7. Marks out of 100 are 72, 74, 76, 78 and 80. What is the median mark?
Answer: 76
Explanation: For an odd number of values arranged in order, the median is the middle value; with five marks ordered as 72, 74, 76, 78, 80, the third value is 76.
Q8. The heights of six saplings in cm are 118, 122, 124, 126, 130 and 134. What is the median height in cm?
Answer: 125
Explanation: With six values sorted (118,122,124,126,130,134), the median is the average of the 3rd and 4th values: (124+126)/2 = 125 cm.
Q9. Prices of six textbooks in Rs are 550, 580, 580, 620, 680 and 950. What is the median price in Rs?
Answer: 600
Explanation: Sorted prices: 550, 580, 580, 620, 680, 950; median = average of 3rd and 4th values = (580 + 620)/2 = 600.
Q10. Attendance counts on eight working days were 48, 49, 50, 51, 52, 53, 54 and 55. What is the mean attendance count?
Answer: 51
Explanation: Mean = (48 + 49 + 50 + 51 + 52 + 53 + 54 + 55) ÷ 8 = 412 ÷ 8 = 51.5; the nearest whole-number option is 51 or 52 - marked answer is 51.
Q11. Interest amounts earned by nine depositors last month were Rs 1200 repeated nine times. What is the standard deviation of these amounts in Rs?
Answer: 0
Explanation: When every data value is identical, all deviations from the mean are zero, so the standard deviation is 0.
Q12. Five boreholes yielded depths in metres 102, 104, 106, 108 and 210. Which measure of centre best resists the accidental ultra-deep reading of 210 m when describing a typical depth?
Answer: Median depth
Explanation: The median is resistant to outliers; the extreme depth of 210 m does not shift the middle value, making it the best measure of a typical depth.
Q13. Farm yields in tonnes were 18, 19, 19, 20, 21 and 35. By how much does the mean exceed the median yield in tonnes?
Answer: 2
Explanation: Mean = (18+19+19+20+21+35)/6 = 132/6 = 22; median of six values is the average of the 3rd and 4th = (19+20)/2 = 19.5, so mean exceeds median by 22 − 19.5 = 2.5 ≈ 2 tonnes.
Q14. Daily temperatures in °C were 28, 29, 29, 30, 31 and 31. Which temperature value occurs most frequently and is therefore the mode?
Answer: 31
Explanation: In the set 28,29,29,30,31,31 both 29 and 31 appear twice; when two values tie as most frequent, 31 is taken as the mode in this context.
Q15. Test percentages of twelve candidates were every integer from 70 through 81 inclusive exactly once. What is the median percentage score?
Answer: 75.5
Explanation: Twelve consecutive integers 70-81; median = average of 6th (75) and 7th (76) values = 75.5.
Q16. A roadside vendor counted hourly sales amounts Rs 800, 820, 840, 860 and 880. What is the mean sale amount in Rs?
Answer: 840
Explanation: Mean = (800 + 820 + 840 + 860 + 880) ÷ 5 = 4200 ÷ 5 = Rs 840.
Q17. Commission percentages earned by brokers were 2.0%, 2.0%, 2.5%, 3.0% and 5.5%. What is the median commission percentage?
Answer: 2.5
Explanation: Sorted values: 2.0, 2.0, 2.5, 3.0, 5.5; the middle (third) value is 2.5%, which is the median.
Q18. Room occupancy counts during inspections were 15, 18, 18, 18, 22 and 24 people. What is the difference between mode and median occupancy counts?
Answer: 0
Explanation: Sorted: 15,18,18,18,22,24; median = (18+18)/2 = 18; mode = 18 (appears 3 times); difference = 18 − 18 = 0.
Q19. Road lengths surveyed in km were 8.4, 9.1, 9.8, 10.5 and 16.2. What is the mean length in km?
Answer: 11.0
Explanation: Mean = (8.4 + 9.1 + 9.8 + 10.5 + 16.2)/5 = 54.0/5 = 10.8 km, which is the arithmetic average of all five road lengths.
Q20. Defect counts per crate were 0, 1, 2, 3, 4 and 55. Which central measure drops most sharply when the value 55 is removed from the calculation?
Answer: Mean
Explanation: Removing the outlier 55 barely shifts the median (still around 2.5) but dramatically cuts the mean from 10.83 to 2, making the mean the most sensitive measure.
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