Question

the data set below represents the total number of touchdowns a quarterback threw each season for 10 seasons of play. 29, 5, 26, 20, 23, 18, 17, 21, 28, 20. 1. order the values: 5, 17, 18, 20, 20, 20, 21, 23, 26, 28, 29. 2. determine the median: \\(\frac{20 + 21}{2}=\frac{41}{2}=20.5\\). calculate the measures of variability for the data set. the range is . the interquartile range is . touchdowns touchdowns

Explanation:

Step1: Order the data

5, 17, 17, 18, 18, 20, 20, 20, 21, 21, 23, 23, 26, 26, 28, 29

Step2: Calculate the range

Range = Maximum - Minimum = 29 - 5 = 24

Step3: Find the median (Q2)

Since there are 16 data - points, the median is the average of the 8th and 9th ordered values. Median = $\frac{20 + 21}{2}=20.5$

Step4: Find Q1

The lower half of the data is 5, 17, 17, 18, 18, 20, 20, 20. Since there are 8 data - points in the lower half, Q1 is the average of the 4th and 5th ordered values in the lower half. Q1=$\frac{18 + 18}{2}=18$

Step5: Find Q3

The upper half of the data is 21, 21, 23, 23, 26, 26, 28, 29. Since there are 8 data - points in the upper half, Q3 is the average of the 4th and 5th ordered values in the upper half. Q3=$\frac{23+26}{2}=24.5$

Step6: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1 = 24.5 - 18 = 6.5

Answer:

Range: 24
Inter - quartile range: 6.5