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Plot A shows theWhich statement correctly compares the measures of center in the two sets of data?

Both the mean and median are greater for Plot A than for Plot B.

Both the mean and median are greater for Plot B than for Plot A.

Plot A has a greater median than Plot B, but Plot B has a greater mean.

Plot B has a greater median than Plot A, but Plot A has a greater mean. number of hours ten girls watched television over a one-week period. Plot B shows the number of hours ten boys watched television over the same period of time.


The two plots, Plot A and Plot B, show dot plots of the number of hours spent watching television by two groups (ten girls in Plot A and ten boys in Plot B). The goal is to compare the measures of center (mean and median) between these two plots.

Let's analyze each:

### **Plot A (Girls)**
- The data points are: 4, 4, 4, 5, 5, 5, 5, 6, 6, 10.
- **Median of Plot A**: The middle two values in this ordered data set are 5 and 5, so the median is 5.
- **Mean of Plot A**:
  \[
  \text{Mean} = \frac{4 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 10}{10} = \frac{54}{10} = 5.4
  \]

### **Plot B (Boys)**
- The data points are: 4, 5, 5, 5, 6, 6, 6, 7, 7, 7.
- **Median of Plot B**: The middle two values are 6 and 6, so the median is 6.
- **Mean of Plot B**:
  \[
  \text{Mean} = \frac{4 + 5 + 5 + 5 + 6 + 6 + 6 + 7 + 7 + 7}{10} = \frac{58}{10} = 5.8
  \]

### **Comparison of Mean and Median**:
- **Median**: Plot A has a median of 5, and Plot B has a median of 6. Therefore, Plot B has a greater median.
- **Mean**: Plot A has a mean of 5.4, and Plot B has a mean of 5.8. Therefore, Plot B also has a greater mean.

### Conclusion:
The correct answer is:
**Both the mean and median are greater for Plot B than for Plot A.**

Would you like more details on the calculation steps or clarification?

Here are five related questions to expand on this:
1. How does the range of data influence the mean and median?
2. What would happen if outliers were present in either data set?
3. Can you explain how the mode differs from the median and mean in this context?
4. How would a symmetrical versus skewed distribution affect the mean and median?
5. What are the advantages of using the median over the mean in certain datasets?

**Tip**: The median is often more resistant to outliers than the mean, making it a better measure of center for skewed distributions.

Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of hours ten boys watched television over the same period of time. Which statement correctly compares the measures of center in the two sets of data?

This problem compares the mean and median of two sets of data showing hours of television watched by boys and girls. Learn how to calculate the mean and median and understand the implications of these measures of center.

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