Civil Service Numerical Reasoning Test Statistical Reasoning — Questions and Answers
Question 1: A team records their daily case completions over 10 days: 12, 15, 11, 14, 18, 13, 16, 12, 15, 14. What is the median number of cases completed per day?
- 13
- 14 (Correct answer)
- 14.5
- 13.5
Correct answer: 14
Sorted: 11, 12, 12, 13, 14, 14, 15, 15, 16, 18. With 10 values, the median is the average of the 5th and 6th values: (14 + 14) / 2 = 14.
Question 2: Customer satisfaction scores for five regional offices are: 72, 85, 68, 91, 74. The mean is 78. What is the sample standard deviation?
- 8.6
- 9.6 (Correct answer)
- 7.8
- 10.1
Correct answer: 9.6
Deviations from mean (78): -6, 7, -10, 13, -4. Squared: 36, 49, 100, 169, 16. Sum of squares = 370. Sample variance = 370 / (5-1) = 92.5. Sample standard deviation = square root of 92.5 = 9.6.
Question 3: A dataset of processing times has a mean of 4.2 days and a standard deviation of 0.8 days. Using the empirical rule, approximately what percentage of cases are processed within 2.6 to 5.8 days?
- 68%
- 95% (Correct answer)
- 99.7%
- 90%
Correct answer: 95%
2.6 days = 4.2 minus 2(0.8) = mean minus 2 standard deviations. 5.8 days = 4.2 + 2(0.8) = mean plus 2 standard deviations. The empirical rule states approximately 95% of data falls within 2 standard deviations of the mean.
Question 4: In a weighted scoring system for supplier evaluation, Quality scores 8/10 (weight 40%), Price scores 7/10 (weight 35%), and Delivery scores 9/10 (weight 25%). What is the weighted total score?
- 7.90 (Correct answer)
- 7.70
- 8.10
- 7.95
Correct answer: 7.90
Weighted score = (8 x 0.40) + (7 x 0.35) + (9 x 0.25) = 3.20 + 2.45 + 2.25 = 7.90.
Question 5: A government survey has a sample size of 1,600 and finds 52% support for a policy. The margin of error is plus or minus 2.5%. What is the confidence interval for the true level of support?
- 49.5% to 54.5% (Correct answer)
- 50.0% to 55.0%
- 47.5% to 56.5%
- 50.5% to 53.5%
Correct answer: 49.5% to 54.5%
Confidence interval = survey result plus or minus margin of error = 52% plus or minus 2.5% = 49.5% to 54.5%. This means we can be confident the true support level falls within this range.
Question 6: Five projects have completion rates of 88%, 92%, 76%, 95%, and 84%. The departmental target is that at least 80% of projects achieve above 85% completion. Does the department meet this target?
- Yes, 60% achieve above 85%
- No, only 60% achieve above 85% (Correct answer)
- Yes, 80% achieve above 85%
- No, only 40% achieve above 85%
Correct answer: No, only 60% achieve above 85%
Projects above 85%: 88%, 92%, 95% = 3 out of 5 = 60%. The target requires 80% of projects (4 out of 5) to exceed 85%. Since only 60% meet the threshold, the department does not meet the target.
Civil Service Numerical Reasoning Test Statistical Reasoning
A team records their daily case completions over 10 days: 12, 15, 11, 14, 18, 13, 16, 12, 15, 14.
What is the median number of cases completed per day?