Mean, Median, and Mode — Probability & Statistics 练习题

Grades 6–8 简单难度 10 道题

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.

练习的技能

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

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练习题：Mean, Median, and Mode

说明： 仔细解答每一道题。清晰地展示所有解题过程。在指定位置或按指示在另一张纸上写出最终答案。

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

Mean, Median, and Mode — 练习题（续）

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 — 练习题（续）

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 — 练习题（续）

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 — 练习题（续）

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 — 练习题（续）

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.

参考答案

1.

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

最终答案： 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: $5$

最终答案： 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: $85$

最终答案： 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: $12$

最终答案： Mean: $15$ , Median: $14$ , Mode: $12$

参考答案（续）

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: $5$

最终答案： 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: $22$

最终答案： 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: $104$

最终答案： 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)

最终答案： 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: $2$

最终答案： Mean: $2.1$ , Median: $2$ , Mode: $2$

参考答案（续）

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: $68$

最终答案： Mean: $70.7$ , Median: $70$ , Mode: $68$

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需要避免的常见错误

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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