IPA IP 2023 Question 77
A question IPA Japan published in 令和5年度 ITパスポート試験 公開問題 問77, translated into English. ITPEC is based on the same exams.
The results of an examination in four (4) subjects taken by 10,000 examinees are as shown in the table, and it is assumed that the score distribution of every subject follows a normal distribution. When the scores of an examinee in the four subjects were all 71 points, which of the following is the subject in which this examinee obtained the highest deviation value?
Unit: Points
Explanation
Mathematics — the same 71 points stands furthest above the average, measured in standard deviations, in Mathematics.
A deviation value (standard score) rescales a score so that the average is 50 and one standard deviation is 10: deviation value = 50 + 10 × (score − average) ÷ standard deviation. The subject with the highest deviation value is therefore the one where (71 − average) ÷ standard deviation is largest:
Because every subject is normally distributed, a larger value also means a smaller share of the 10,000 examinees scored above 71 in that subject.
Answer (c)
Why not others:
- •(a) Japanese — the smallest spread (5) makes 9 points worth 1.80 standard deviations, close to but below Mathematics’ 2.17
- •(b) Social studies — the biggest lead in raw points (16), but the widest spread (9) shrinks it to 1.78 standard deviations
- •(d) Science — 11 points over a spread of 7 is only 1.57 standard deviations, the lowest of the four
Key rule: To compare scores from tests with different averages and spreads, divide the distance from the average by the standard deviation; raw points or the distance alone mislead.
Basic Theory · AI-written, may contain errors
This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.