Question

CAN SOMEONE HELP ASAP?

The following table shows the number of hours some high school students in two states spend surfing the Internet each week:


State A 35 36 35 34 35 38 36 36 38
State B 24 22 20 50 25 24 65 25 26


Part A: Create a five-number summary and calculate the interquartile range for the two sets of data.

Part B: Are the box plots symmetric? Justify your answer.

Answer 1

Arrange the data set in ascending order:
State A: 34, 35, 35, 35, 36, 36, 36, 38, 38
State B: 20, 22, 24, 24, 25, 25, 26, 50, 65

5 number summary
                            State A            State B
1) minimum           34                     20
2) 1st quartile        35                     23
3) median              36                     25
4) 3rd quartile        38                     50
5) maximum          38                     65
IQR = Q3 - Q1         3                     27

The box plots are not symmetric. The median should be equally distanced from the 1st quartile and the 3rd quartile for the box plot to be symmetric.

Answer 2

The correct answers are:

Part A: For State A, the median is 36; Q1 is 35; Q3 is 37; the lowest value is 34; and the highest value is 38. For State B, the median is 25; Q1 is 23; Q3 is 38; the lowest value is 26; and the highest value is 65.

Part B: State A has a symmetric box plot; State B does not.

Explanation:

To find the five number summary for each set, we must first order the numbers from least to greatest:

State A: 34, 35, 35, 35, 36, 36, 36, 38, 38

The median is the middle value. We can see this is 36. Q1 is the value halfway between the median and the lowest value (do not include the median in this list); this is between 35 and 35, which is 35. Q3 is the value halfway between the median and the highest value (do not include the median in this list); this is between 36 and 38, which is 37. The lowest value is 34, and the highest value is 38. This is a symmetric plot, since there is 1 unit between the lowest value and Q1; 1 unit between Q1 and the median; 1 unit between the median and Q3; and 1 unit between Q3 and the highest value.

For State B: 20, 22, 24, 24, 25, 25, 26, 50, 65

The median, or middle value, is 25. Q1, halfway between the median and the lowest value, is 23 (between 22 and 24). Q3, halfway between the median and the highest value, is 38 ((26+50)/2 = 76/2 = 38). The highest value is 65 and the lowest value is 20. This box plot is not symmetric; this is because there are 3 units from the lowest value to Q1, 2 units from Q1 to the median, 13 units from the median to Q3, and 27 units from Q3 to the highest value.