Final answer:
After organizing the income data, calculating the five-number summary, and identifying the quartiles, we find that we cannot determine the correct box and whisker plot without the visual options. However, the income data must have a minimum of $49,781, Q1 of $57,242, a median of $64,475, Q3 of $72,923, and a maximum of $86,345 for it to be correct.
Step-by-step explanation:
To determine which box and whisker plot correctly represents the median household incomes for 20 U.S. states, we must calculate the five-number summary: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
- First, we put the data in ascending order.
- Next, we find the minimum and maximum values in the data set, which are $49,781 and $86,345, respectively.
- Since there are 20 data points, to find the median, we take the average of the 10th and 11th values, which are $63,938 and $65,012, so the median is $(63,938 + 65,012) / 2 = $64,475.
- For Q1, we find the median of the first 10 data points, which is the average of the 5th and 6th values, or $(55,821 + 58,663) / 2 = $57,242.
- For Q3, we find the median of the last 10 data points, which is the average of the 15th and 16th values, or $(72,812 + 73,034) / 2 = $72,923.
- Now, with the five-number summary, we can identify the correct box and whisker plot which should have the minimum at $49,781, Q1 at $57,242, a median at $64,475, Q3 at $72,923, and a maximum at $86,345.
Without the provided plots, we cannot determine which of the box and whisker plots (A, B, C, or D) is the correct one, but the correct plot must match the five-number summary calculated above.