PLEASE HELP ASAP!!! 40 POINTS!!
A comparative box plot for two data sets is shown.

Two box-and-whisker plots. The first is titled, Set A, with left whisker 20, right whisker 26, left hand side of box 23.5, right hand side of box 25.5, and median 24. The second is titled, Set B, with left whisker 13, right whisker 23, left hand side of box 14.5, right hand side of box 16.5, and median 15.5.

Which statement is true?

Question 1 options:

At least 75% of the data is greater than 23.

More than 50% of the data for each set is between 20 and 23.

No more than 25% of the data for the sets overlap.

More than 25% of the data for each set is greater than 20.

A box and whisker plot (also known as a "box plot"), is a graph displaying the distribution of a set of data based on a five number summary.

Five-number summary

Minimum value = The value at the end of the left whisker.
Lower quartile (Q₁) = The left side of the box.
Median (Q₂) = The vertical line inside the box.
Upper quartile (Q₃) = The right side of the box
Maximum = The value at the end of the right whisker.

Therefore, the five-number summaries for Set A and Set B are:

Set A

Minimum = 20
Q1 = 23.5
Median = 24
Q3 = 25.5
Maximum = 26

Set B

Minimum = 13
Q1 = 14.5
Median = 15.5
Q3 = 16.5
Maximum = 23

In terms of percentages of data:

The median divides the data into two equal halves, with 50% of the data falling below and 50% above it.
The first quartile (Q1) marks the boundary below which 25% of the data falls.
The third quartile (Q3) marks the boundary below which 75% of the data falls.
The interquartile range (IQR) is between the first quartile (Q1) and the third quartile (Q3). It contains the middle 50% of the data.

Answer option a

The maximum data value in Set B is 23, so this means 100% of the data in Set B is 23 or less.

Therefore, the statement "At least 75% of the data is greater than 23" is untrue.

Answer option b

In Set A, the data values between 20 and 23 are contained between the minimum value and Q1 (the first 25% of the data values).

In Set B, the data values between 20 and 23 are contained between Q3 and the maximum value (the last 25% of the data values).

Therefore, up to 25% of the data for each set is between 20 and 23.

Therefore, the statement "More than 50% of the data for each set is between 20 and 23" is untrue.

Answer option c

Part of the lower 25% of Set A (minimum value to Q1) and part of the upper 25% of Set B (Q3 to maximum value) overlap. So no more than 25% of the data for the sets overlap.

Therefore, the statement "No more than 25% of the data for the sets overlap" is true.

Answer option d

The data value 20 falls in the top 25% of Set B, so up to 25% of the data is greater than 20. So no more than 25% of the data for Set B is greater than 20.

Therefore, the statement "More than 25% of the data for each set is greater than 20" is untrue.