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.