Question

Andre, Lin, and Noah each designed and built a paper airplane. They launched each plane several times and recorded the distance of each flight in yards. Write the five-number summary for the data for each airplane. Then, calculate the interquartile range for each data set.

Answer 1

Andre's: Min = 18, Q1 = 23.5, Median = 28.5, Q3 = 31.5, Max = 35, IQR = 8

Lin's: Min = 15, Q1 = 19, Median = 21.5, Q3 = 24, Max = 33, IQR = 5

Noah's: Min = 10, Q1 = 12.5, Median = 19, Q3 = 22.5, Max = 25, IQR = 10

Explanation:

Answer 2

Let's say the distances recorded for each airplane are:

Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35
Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33
Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25

To find the five-number summary for each data set, we need to find the minimum, maximum, median, and quartiles. We can start by ordering the data sets from smallest to largest:

Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35
Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33
Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25

Minimum:
Andre's: 18
Lin's: 15
Noah's: 10

Maximum:
Andre's: 35
Lin's: 33
Noah's: 25

Median:
Andre's: (28 + 29) / 2 = 28.5
Lin's: (21 + 22) / 2 = 21.5
Noah's: (18 + 20) / 2 = 19

First Quartile (Q1):
Andre's: (22 + 25) / 2 = 23.5
Lin's: (18 + 20) / 2 = 19
Noah's: (12 + 13) / 2 = 12.5

Third Quartile (Q3):
Andre's: (31 + 32) / 2 = 31.5
Lin's: (23 + 25) / 2 = 24
Noah's: (22 + 23) / 2 = 22.5

Interquartile Range (IQR):
IQR = Q3 - Q1
Andre's: 31.5 - 23.5 = 8
Lin's: 24 - 19 = 5
Noah's: 22.5 - 12.5 = 10

So the five-number summary and interquartile range for each data set are:

Andre's: Min = 18, Q1 = 23.5, Median = 28.5, Q3 = 31.5, Max = 35, IQR = 8
Lin's: Min = 15, Q1 = 19, Median = 21.5, Q3 = 24, Max = 33, IQR = 5
Noah's: Min = 10, Q1 = 12.5, Median = 19, Q3 = 22.5, Max = 25, IQR = 10