https://file.aiquickdraw.com/mathbot/file/1726844190959441epaa5.jpg

Let's analyze the provided data from the image:

1. **Department Store A (Histogram)**: The price distribution is shown in four price ranges: 
   - 0 to $4.99: About 12 items
   - $5 to $9.99: About 6 items
   - $10 to $14.99: About 8 items
   - $15 to $19.99: About 4 items

2. **Department Store B (Box Plot)**: 
   - The minimum price is around $2.
   - The first quartile (Q1) is about $6.
   - The median (Q2) is around $12.
   - The third quartile (Q3) is about $16.
   - The maximum price is about $20.

### Evaluating the statements:

1. **The median price at Department Store A is greater than the median price of Department Store B**:  
   - **False**: The histogram suggests the median price in Store A falls between $5 and $9.99, which is less than the median price at Store B (about $12).

2. **The median price at Department Store B is greater than the median price at Department Store A**:  
   - **True**: The median at Store B is $12, while at Store A, it is less than $10.

3. **A greater percentage of items are under $5 at Department Store B than at Department Store A**:  
   - **False**: In Store A, about 12 items (out of 30) are priced below $5, which is 40%. From the box plot of Store B, fewer items are likely priced under $5, as the first quartile is around $6.

4. **50% of the items in Department Store A are priced between $5 and $14.99, inclusively**:  
   - **True**: Roughly half of the items in Store A fall between $5 and $14.99 (about 6 items in $5-$9.99 and 8 items in $10-$14.99).

5. **50% of the items in Department Store B are priced between $6 and $16, inclusively**:  
   - **True**: Based on the box plot, the interquartile range (Q1 to Q3) is from $6 to $16, meaning 50% of items are within this range.

### Correct answers:
- The second, fourth, and fifth statements are correct.

Would you like further clarifications or details?

Here are 5 additional questions you could explore:
1. How do you calculate the interquartile range for Store B?
2. What does the box plot suggest about the variability of prices in Store B compared to Store A?
3. Could you estimate the mean price of items in Store A based on the histogram?
4. What would happen to the analysis if the distribution in Store A were more uniform?
5. How would outliers in Store B affect the interpretation of its price distribution?

**Tip**: Box plots are great for visualizing the spread and center of data, but they may not show the frequency of values within each range clearly.

Analyze the pricing data for Department Stores A and B using the given histogram and box plot. Determine which statements about the prices are true.

Learn how to compare pricing data between two department stores using a histogram and a box plot. Understand key concepts such as the median, interquartile range, and price distributions. Perfect for students in Grades 6-9, this problem explores how to determine which store has higher prices based on visual data representation.

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