Mean, Median, and Mode — Probability & Statistics Übungsblatt

Grades 6–8 Leichter Schwierigkeitsgrad 10 Aufgaben

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.

Geübte Fähigkeiten

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

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Übungsblatt: Mean, Median, and Mode

Anleitung: Löse jede Aufgabe sorgfältig. Zeige deine Arbeit klar. Schreibe deine endgültige Antwort in das vorgesehene Feld oder wie angewiesen auf ein separates Blatt.

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

Mean, Median, and Mode — Übungsblatt (Fortsetzung)

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 — Übungsblatt (Fortsetzung)

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 — Übungsblatt (Fortsetzung)

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 — Übungsblatt (Fortsetzung)

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 — Übungsblatt (Fortsetzung)

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.

Lösungsschlüssel

1.

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

Endgültige Antwort: 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: $5$

Endgültige Antwort: 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: $85$

Endgültige Antwort: 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: $12$

Endgültige Antwort: Mean: $15$ , Median: $14$ , Mode: $12$

Lösungsschlüssel (Fortsetzung)

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: $5$

Endgültige Antwort: 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: $22$

Endgültige Antwort: 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: $104$

Endgültige Antwort: 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)

Endgültige Antwort: 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: $2$

Endgültige Antwort: Mean: $2.1$ , Median: $2$ , Mode: $2$

Lösungsschlüssel (Fortsetzung)

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: $68$

Endgültige Antwort: Mean: $70.7$ , Median: $70$ , Mode: $68$

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Häufige Fehler, die es zu vermeiden gilt

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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