Here are five examples illustrating how to calculate the mean, median, and mode for different sets of numbers:

Example 1

Data Set: $4, 7, 8, 12, 14$

1. Mean: Add all values and divide by the number of values: $\text{Mean} = \frac{4 + 7 + 8 + 12 + 14}{5} = 9$
2. Median: Middle value (since there are 5 values, it's the third one): $\text{Median} = 8$
3. Mode: No value repeats, so there is no mode.

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Example 2

Data Set: $10, 15, 15, 20, 25$

1. Mean: $\text{Mean} = \frac{10 + 15 + 15 + 20 + 25}{5} = 17$
2. Median: Middle value is 15. $\text{Median} = 15$
3. Mode: 15 (it appears most frequently).

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Example 3

Data Set: $2, 3, 3, 3, 5, 8$

1. Mean: $\text{Mean} = \frac{2 + 3 + 3 + 3 + 5 + 8}{6} = 4$
2. Median: The middle values are the third and fourth values (both 3): $\text{Median} = \frac{3 + 3}{2} = 3$
3. Mode: 3 (it appears most frequently).

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Example 4

Data Set: $22, 26, 28, 30, 34, 34, 36$

1. Mean: $\text{Mean} = \frac{22 + 26 + 28 + 30 + 34 + 34 + 36}{7} \approx 30$
2. Median: The middle value (fourth) is 30. $\text{Median} = 30$
3. Mode: 34 (it appears twice).

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Example 5

Data Set: $1, 1, 2, 3, 3, 4, 4, 4$

1. Mean: $\text{Mean} = \frac{1 + 1 + 2 + 3 + 3 + 4 + 4 + 4}{8} = 2.75$
2. Median: Middle values are 3 and 3. $\text{Median} = \frac{3 + 3}{2} = 3$
3. Mode: 4 (it appears most frequently).

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Would you like more detailed explanations for any of these calculations?

Related Questions

1. How are mean, median, and mode different from each other in interpretation?
2. What are the effects of outliers on mean, median, and mode?
3. Can a data set have more than one mode?
4. How is median calculated in an even-numbered data set?
5. Why might median be preferred over mean in some cases?

Tip

When a data set has outliers, the median is often a better measure of central tendency than the mean because it is less affected by extreme values.