the prices of items in the holiday gift section of department store a are given in the histogram. the prices…

the prices of items in the holiday gift section of department store a are given in the histogram. the prices of the same items in department store b are given in the box plot. which statement must be true? the median price at department store a is greater than the median price at department store b the median price at department store b is greater than the median price at department store a. the range of prices is wider at department store b than the ranges of prices at department store a a greater percentage of items are less than $5 at department store b than at department store a.

the prices of items in the holiday gift section of department store a are given in the histogram. the prices of the same items in department store b are given in the box plot. which statement must be true? the median price at department store a is greater than the median price at department store b the median price at department store b is greater than the median price at department store a. the range of prices is wider at department store b than the ranges of prices at department store a a greater percentage of items are less than $5 at department store b than at department store a.

Answer

Explanation:

Step1: Analyze median of Store A

From the histogram of Store A, assume total number of items is (n = 12 + 8+10 + 4=34). Since (n = 34) (even - numbered data - set), the median is the average of the 17th and 18th ordered data - points. The first 12 items are in the (0 - 4.99) range, and the next 8 items are in the (5 - 9.99) range. The 17th and 18th items fall into the (5 - 9.99) range. So the median of Store A is in the (5 - 9.99) range.

Step2: Analyze median of Store B

From the box - plot of Store B, the median is the value at the vertical line inside the box. The box - plot shows that the median of Store B is around 8.

Step3: Analyze range of Store A

The range of Store A is from (0) to (19.99), so range (R_A=19.99 - 0=19.99).

Step4: Analyze range of Store B

The range of Store B is from the minimum value (left - most whisker) to the maximum value (right - most whisker). From the box - plot, the minimum is around (2) and the maximum is around (16), so range (R_B = 16 - 2=14).

Step5: Analyze percentage of items less than $5

In Store A, the number of items less than (5) is (12). The proportion of items less than (5) in Store A is (\frac{12}{34}\approx0.353). In Store B, from the box - plot, the first quartile ((Q_1)) is around (4), which means 25% of the data is less than (4). So the proportion of items less than (5) in Store B is less than 25%.

Since the median of Store A is in the (5 - 9.99) range and the median of Store B is around 8, the median price at Department Store B is greater than the median price at Department Store A.

Answer:

The median price at Department Store B is greater than the median price at Department Store A.