ITPEC IP April 2023 Question 4
Which of the following is the combination of the mean and median of the data?
[Data]
10, 20, 20, 20, 40, 50, 100, 440, 2000
Explanation
Mean 300, median 40 — the mean divides the total by the count; the median is the middle value of the sorted data.
- •Total: 10 + 20 + 20 + 20 + 40 + 50 + 100 + 440 + 2000 = 2700
- •Mean: 2700 ÷ 9 = 300
- •Median: the nine values are already sorted, so the median is the 5th: 40
The two large values, 440 and 2000, pull the mean far above the median; the median depends only on the middle position.
Answer (d)
Why not others:
- •(a) 20, 40 — 20 is the mode, the most frequent value, not the mean
- •(b) 40, 20 — takes the median as the mean and the mode as the median
- •(c) 300, 20 — the mean is right, but 20 is the mode; the middle (5th) value is 40
Key rule: With skewed data the mean, median and mode split apart: a few very large values drag the mean up while the median stays at the middle position.
Basic Theory · AI-written, may contain errors
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