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### Question 5 (Dot plot: Number of books read by students)

#### a. **Which measure of center would you use given the shape of the distribution in the dot plot? Explain your reasoning. Calculate the appropriate measure of center.**

**Answer:**
The distribution in the dot plot is **skewed to the right** (there are more values clustered on the left side, and a few outliers on the right). For a skewed distribution, the **median** is the best measure of center because it is less affected by extreme values.

To find the median:
- Count the number of data points. There are **13** students.
- The median is the **middle value**, which is the 7th data point when arranged in order.

From the dot plot, the 7th point corresponds to **7 books**.

So, the **median** is **7 books**.

#### b. **Which measure of variability would you use? Explain your reasoning. Calculate the appropriate measure of variability.**

**Answer:**
For skewed data, the **interquartile range (IQR)** is the best measure of variability because it focuses on the middle 50% of the data and ignores the outliers.

To calculate the IQR:
- Arrange the data in order.
- Find the **1st quartile (Q1)** (the median of the first half of the data) and the **3rd quartile (Q3)** (the median of the second half).

Looking at the data, we can estimate:
- **Q1** (middle of the first half) is **6 books**.
- **Q3** (middle of the second half) is **9 books**.

So, the **IQR** = Q3 - Q1 = **9 - 6 = 3** books.

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### Question 6 (Dot plot: Number of families living in blocks)

#### a. **Which measure of center would you use given the shape of the distribution in the dot plot? Explain your reasoning. Calculate the appropriate measure of center.**

**Answer:**
The distribution here is approximately **symmetrical**. When the distribution is roughly symmetrical, the **mean** is a good measure of center.

To find the mean:
- Add up the total number of families: \( 3+4+5+5+6+6+7+7+8+8+9+10+11 = 89 \).
- Count the number of data points. There are **13** blocks.

Mean = Total families / Number of blocks = \( 89 / 13 ≈ 6.85 \).

So, the **mean** number of families is approximately **6.85 families**.

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Let me know if you'd like further clarifications, or have any questions! Here are 5 related questions to expand your understanding:

1. What are the key differences between mean and median when analyzing a data set?
2. How does skewness affect the choice of measure of center?
3. Can outliers affect the interquartile range (IQR)? Why or why not?
4. How would the analysis change if the distribution was more symmetrical in Question 5?
5. What is the difference between range and interquartile range as measures of variability?

**Tip:** When analyzing data, always first look at the shape of the distribution before deciding whether to use the mean or median!

The dot plot displays the number of books read by students during the semester and the number of families living in different blocks of a town. The questions ask about the measure of center and variability based on the shape of the distributions.

This problem involves analyzing dot plots to find the appropriate measure of center and variability. For skewed data distributions, the median and interquartile range (IQR) are used, while the mean is used for symmetrical distributions. Learn how to calculate the center and variability for data on books read by students and families in different town blocks.

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