令和4年度 ITパスポート試験問59

This question's explanation and your answers so far.

問59

頻出度★★☆

次のデータの平均値と中央値の組合せはどれか。〔データ〕 10, 20, 20, 20, 40, 50, 100, 440, 2000

	平均値	中央値
ア	20	40

	平均値	中央値
イ	40	20

	平均値	中央値
ウ	300	20

	平均値	中央値
エ	300	40

出典　令和4年度 ITパスポート試験問59

解説

問 59

Incorrectア
This option gives mean = 20 and median = 40, but the mean is actually 300, so it is wrong. 20 corresponds to the mode (the most frequently occurring value), not the mean.
Incorrectイ
This option gives mean = 40 and median = 20, but both the mean and the median differ from the actual values. In reality the mean = 300 and the median = 40, so both are wrong.
Incorrectウ
The mean = 300 is correct, but giving the median as 20 is wrong. The median is the 5th value, so it is 40, not 20.
エ
正解 The data are 10, 20, 20, 20, 40, 50, 100, 440, 2000, nine values in total. The mean is the sum of all data divided by the number of data: the sum is 2700 and the count is 9, so the mean = 2700 ÷ 9 = 300. The median is the value at the center when the data are arranged in ascending order; with 9 values it is the 5th value. The data are already in ascending order and the 5th value is 40, so the median = 40. Therefore the combination is mean = 300 and median = 40, and the correct answer is エ.

ここがポイント

Mean = sum of the data ÷ number of data. When there is an extremely large value such as 2000 (an outlier), the mean is pulled up significantly.
Median = the central value when the data are arranged in ascending order. When the number of data is an odd number n, it is the (n+1)/2-th value, and it is less affected by outliers.

用語

解答問59エ