Civil Service Numerical Reasoning Test Statistical Reasoning

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?

Accepted Answer

14

Answer

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?

Accepted Answer

9.6

Answer

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?

Accepted Answer

95%

Answer

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?

Accepted Answer

7.90

Answer

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?

Accepted Answer

49.5% to 54.5%

Answer

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.

Civil Service Numerical Reasoning Practice Test

Civil Service Numerical Reasoning Practice Test

Civil Service Numerical Reasoning Test Statistical Reasoning