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A fashion analyst measures the number of pairs of shoes owned by 14 individuals with various incomes. Based on the data above, which of the following is true?

(A) The mean number of shoe pairs level is greater than the range of the number of shoe pairs data.

(B) The mean number of shoe pairs is less than the median number of shoe pairs.

(C) The median number of shoe pairs is greater than the range of the number of shoe pairs.

(D) The range of the number of shoe pairs data is greater than the mode number of shoe pairs.

To analyze the data from the scatterplot and answer the multiple-choice question, we need to compute or estimate the following statistics for the number of pairs of shoes owned by the 14 individuals:

1. **Range**: The difference between the maximum and minimum values of the number of shoes.
2. **Mean**: The average number of shoe pairs.
3. **Median**: The middle value of the shoe data set when ordered from smallest to largest.
4. **Mode**: The most frequently occurring number of shoe pairs.

### Step-by-Step Approach:

- The **x-axis** represents annual income, and the **y-axis** represents the number of shoe pairs owned. We're only concerned with the number of shoe pairs for this analysis.
  
#### Estimating Values from the Plot:
Looking at the scatterplot:

- **Minimum number of shoe pairs**: From the points, the smallest value appears to be around **2** pairs.
- **Maximum number of shoe pairs**: The largest value is near **45** pairs.

Thus, the **range** is:
\[
\text{Range} = 45 - 2 = 43
\]

#### Counting Data Points:
There are **14 data points**, so we can estimate the mean, median, and mode from the distribution of these points.

- The **mean** would be calculated by summing the number of shoe pairs and dividing by 14, but from a visual inspection, most of the points appear below 15, with a few outliers around 45. Thus, the mean is expected to be relatively low.

- The **median** is the middle value in the ordered list. Visual inspection suggests that the median would likely fall between 10 and 15 pairs of shoes.

- The **mode** is hard to determine precisely, but it seems there is no strongly dominant mode, meaning no number of shoe pairs is repeated frequently.

### Now, let's evaluate the options:

**(A)** The mean number of shoe pairs is greater than the range of the number of shoe pairs.

- This seems unlikely. The range is 43, and the mean is likely well below this based on the distribution of points.

**(B)** The mean number of shoe pairs is less than the median number of shoe pairs.

- This could be plausible if there are high outliers, which would raise the median compared to the mean.

**(C)** The median number of shoe pairs is greater than the range of the number of shoe pairs.

- The median is likely around 10-15, which is much less than the range of 43. So, this statement is false.

**(D)** The range of the number of shoe pairs is greater than the mode number of shoe pairs.

- This seems plausible. The range is 43, and there is no clear mode, meaning the mode is likely low or undefined, making this statement true.

### Conclusion:
The correct answer is likely **(D)**: The range of the number of shoe pairs data is greater than the mode number of shoe pairs.

Would you like more detailed calculations or explanations for this question? Here are some related questions:

1. How do we accurately calculate the mean from a scatterplot?
2. Why is the median less affected by outliers than the mean?
3. How does the mode differ from the mean and median in this context?
4. What is the impact of outliers on the range in a data set?
5. How can we estimate statistical values from a scatterplot like this one?

**Tip**: When analyzing data from scatterplots, always consider how outliers might affect the mean, median, and range differently!

A fashion analyst measures the number of pairs of shoes owned by 14 individuals with various incomes. Based on the data above, which of the following is true? (A) The mean number of shoe pairs level is greater than the range of the number of shoe pairs data. (B) The mean number of shoe pairs is less than the median number of shoe pairs. (C) The median number of shoe pairs is greater than the range of the number of shoe pairs. (D) The range of the number of shoe pairs data is greater than the mode number of shoe pairs.

Analyze the relationship between annual income and the number of shoe pairs owned by individuals. This problem covers descriptive statistics concepts such as mean, median, mode, and range. Suitable for students in Grades 9-11.

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