Question

HELP PLEASE !!!

!A middle school recorded the following donations received during its fundraiser for the school's band:


$23, $18, $25, $43, $50, $16, $22, $32


Part A: Describe the five-number summary of the data set and what each value represents in the context of the problem.


Part B: Which of the box plots shown represents the data set from Part A? Explain why you chose it.

Answer 1

Part A:

The five-number summary of the data set is:
Minimum: $16 - This is the smallest donation amount received.
First quartile (Q1): $20 - This is the median of the lower half of the data set, representing the point below which 25% of the donations fall.
Median (Q2): $23 - This is the middle value of the data set, separating the lower 50% from the upper 50% of donations received.
Third quartile (Q3): $32 - This is the median of the upper half of the data set, representing the point below which 75% of the donations fall.
Maximum: $50 - This is the largest donation amount received.

Part B:

To determine which box plot represents the data set from Part A, we need to consider the values of the five-number summary. Among the given box plots, the one that should be chosen is the box plot with the following characteristics:
- The minimum value on the plot is $16.
- The maximum value on the plot is $50.
- The box on the plot spans from Q1 ($20) to Q3 ($32) and includes the median ($23).

Therefore, the box plot that represents the data set from Part A is the one that satisfies the above conditions.