Mean, Median, and Mode — Probability & Statistics 練習ワークシート

Grades 6–8 かんたん 10問

Measures of center describe the "typical" value in a data set. The mean (average) is the sum divided by the count. The median is the middle value when data is ordered. The mode is the most frequent value.

The range (max $-$ min) measures spread, not center. When data has outliers, the median is often more representative than the mean — consider housing prices or income data.

For an even number of values, the median is the average of the two middle values. A data set can have no mode, one mode, or multiple modes.

練習するスキル

Calculating mean, median, and mode
Finding range
Choosing the best measure of center
Interpreting data in context

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練習ワークシート：Mean, Median, and Mode

指示： 各問題を丁寧に解きましょう。途中式もはっきりと書きましょう。最終的な答えは、指定された場所または指示に従って別の用紙に書いてください。

1.Find the mean, median, and mode of the following data set: $4, 7, 8, 8, 10, 12, 15$

Mean, Median, and Mode — 練習ワークシート（続き）

2.Find the mean, median, and mode of the following data set: $2, 3, 5, 5, 5, 9, 11, 13$
3.The test scores for a class of 8 students are: $72, 85, 91, 85, 68, 74, 85, 90$ Find the mean, median, and mode of these scores.

Mean, Median, and Mode — 練習ワークシート（続き）

4.A basketball player scored the following points in 6 games: $12, 15, 20, 12, 18, 13$ Find the mean, median, and mode.
5.Find the mean, median, and mode of the following data set: $1, 1, 2, 3, 4, 5, 5, 5, 6, 7$

Mean, Median, and Mode — 練習ワークシート（続き）

6.The ages (in years) of 7 people in a room are: $22, 25, 22, 30, 22, 28, 35$ Find the mean, median, and mode.
7.Find the mean, median, and mode of the following data set: $100, 102, 104, 104, 106, 108, 110$

Mean, Median, and Mode — 練習ワークシート（続き）

8.The number of books read by 5 students over summer break: $3, 7, 2, 8, 5$ Find the mean, median, and mode.
9.Find the mean, median, and mode of the following data set: $0, 0, 1, 2, 2, 2, 3, 4, 5$

Mean, Median, and Mode — 練習ワークシート（続き）

10.The daily high temperatures (in $^\circ$ F) for one week were: $68, 72, 75, 68, 70, 74, 68$ Find the mean, median, and mode.

解答集

1.

Mean: $\frac{4+7+8+8+10+12+15}{7} = \frac{64}{7} \approx 9.1$ ; Median: $8$ (4th value); Mode: $8$

最終回答： Mean: $9.1$ , Median: $8$ , Mode: $8$
2.

Mean: $\frac{2+3+5+5+5+9+11+13}{8} = \frac{53}{8} = 6.625 \approx 6.6$ ; Median: $\frac{5+5}{2} = 5$ ; Mode: $5$

最終回答： Mean: $6.6$ , Median: $5$ , Mode: $5$
3.

Data: $68, 72, 74, 85, 85, 85, 90, 91$ (sorted); Mean: $\frac{72+85+91+85+68+74+85+90}{8} = \frac{650}{8} = 81.25 \approx 81.3$ ; Median: $\frac{85+85}{2} = 85$ ; Mode: $85$

最終回答： Mean: $81.3$ , Median: $85$ , Mode: $85$
4.

Data: $12, 12, 13, 15, 18, 20$ (sorted); Mean: $\frac{12+15+20+12+18+13}{6} = \frac{90}{6} = 15$ ; Median: $\frac{13+15}{2} = 14$ ; Mode: $12$

最終回答： Mean: $15$ , Median: $14$ , Mode: $12$

解答集（続き）

5.

Mean: $\frac{1+1+2+3+4+5+5+5+6+7}{10} = \frac{39}{10} = 3.9$ ; Median: $\frac{4+5}{2} = 4.5$ ; Mode: $5$

最終回答： Mean: $3.9$ , Median: $4.5$ , Mode: $5$
6.

Data: $22, 22, 22, 25, 28, 30, 35$ (sorted); Mean: $\frac{22+25+22+30+22+28+35}{7} = \frac{184}{7} \approx 26.3$ ; Median: $25$ (4th value); Mode: $22$

最終回答： Mean: $26.3$ , Median: $25$ , Mode: $22$
7.

Mean: $\frac{100+102+104+104+106+108+110}{7} = \frac{734}{7} \approx 104.9$ ; Median: $104$ (4th value); Mode: $104$

最終回答： Mean: $104.9$ , Median: $104$ , Mode: $104$
8.

Data: $2, 3, 5, 7, 8$ (sorted); Mean: $\frac{3+7+2+8+5}{5} = \frac{25}{5} = 5$ ; Median: $5$ (3rd value); Mode: No mode (all values appear once)

最終回答： Mean: $5$ , Median: $5$ , Mode: No mode
9.

Mean: $\frac{0+0+1+2+2+2+3+4+5}{9} = \frac{19}{9} \approx 2.1$ ; Median: $2$ (5th value); Mode: $2$

最終回答： Mean: $2.1$ , Median: $2$ , Mode: $2$

解答集（続き）

10.

Data: $68, 68, 68, 70, 72, 74, 75$ (sorted); Mean: $\frac{68+72+75+68+70+74+68}{7} = \frac{495}{7} \approx 70.7$ ; Median: $70$ (4th value); Mode: $68$

最終回答： Mean: $70.7$ , Median: $70$ , Mode: $68$

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避けるべきよくある間違い

Forgetting to order data before finding the median
Confusing mean with median
Reporting mode when no value repeats
Including the wrong count when calculating mean

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