Questions: Question 11 0 / 2 pts 100 99 Details Data: 5,7,7,9,9,10,11,11,12,14,14,19,19,19,20 Once you know how to calculate the 5 -number summary, a "box-and-whisker plot" (also called boxplot) is simply a graphical display of the 5 -number summary. a) Based on the boxplot or data above, identify the 5 number summary (min, Q1, median, Q3, max). Observe the connection between the data, the 5 -number summary, and the structure of the boxplot. b) Calculate the range (max - min): c) Calculate the interquartile range (Q3-Q1):

Question 11
0 / 2 pts
100
99
Details

Data: 5,7,7,9,9,10,11,11,12,14,14,19,19,19,20

Once you know how to calculate the 5 -number summary, a "box-and-whisker plot" (also called boxplot) is simply a graphical display of the 5 -number summary.
a) Based on the boxplot or data above, identify the 5 number summary (min, Q1, median, Q3, max).

Observe the connection between the data, the 5 -number summary, and the structure of the boxplot.

b) Calculate the range (max - min):

c) Calculate the interquartile range (Q3-Q1):

Transcript text: Question 11 $0 / 2$ pts 100 99 Details Data: $5,7,7,9,9,10,11,11,12,14,14,19,19,19,20$ Once you know how to calculate the 5 -number summary, a "box-and-whisker plot" (also called boxplot) is simply a graphical display of the 5 -number summary. a) Based on the boxplot or data above, identify the 5 number summary ( min, Q1, median, Q3, max). Observe the connection between the data, the 5 -number summary, and the structure of the boxplot. $\square$ $\square$ $\square$ $\square$ b) Calculate the range ( $\max -\mathrm{min})$ : $\square$ c) Calculate the interquartile range $(\mathrm{Q} 3-\mathrm{Q} 1)$ : $\square$

Solution

Solution Steps

Step 1: Identify the 5-number summary

The 5-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

Given data: 5, 7, 7, 9, 9, 10, 11, 11, 12, 14, 14, 14, 19, 19, 19, 20

Minimum (min): The smallest number in the data set is 5.
First Quartile (Q1): The median of the first half of the data. The first half is 5, 7, 7, 9, 9, 10, 11, 11. The median of this subset is 9.
Median: The middle number of the data set. The data set has 16 numbers, so the median is the average of the 8th and 9th numbers: (11 + 12) / 2 = 11.5.
Third Quartile (Q3): The median of the second half of the data. The second half is 12, 14, 14, 14, 19, 19, 19, 20. The median of this subset is 14.
Maximum (max): The largest number in the data set is 20.

Step 2: Calculate the range

The range is the difference between the maximum and minimum values.

\[ \text{Range} = \text{max} - \text{min} = 20 - 5 = 15 \]

Step 3: Calculate the interquartile range (IQR)

The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1).

\[ \text{IQR} = Q3 - Q1 = 14 - 9 = 5 \]