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Find the range and interquartile range of the data below.

13, 14, 15, 18, 19, 19, 19, 20

Question 2 options:

range = 7

IQR = 5

range = 20

IQR = 4

range = 7

IQR = 4.5

range = 13 to 20

IQR = 14.5 to 19

Verified Answer :

Phylicia

To find the range you subtract the largest number from the smallest 20-13=7. To find the interquartile range you have to find the median of the data set. The median is 18.5, now there are two sets split in half. The median for the lower quartile is 14.5 and the median for the upper quartile is 19. Range=7 and IQR=18.5-14.5=4. IQR=4

Answer:

Option c. Range = 7 IQR = 4.5

Step-by-step explanation:

We have to find the range and interquartile range of the data below :

13, 14, 15, 18, 19, 19, 19, 20

Range: The range of set of data is the difference between the highest and the lowest values of the data set.

Range = Highest value - lowest value

Range = 20 - 13 = 7

Interquartile range (IQR): To find the IQR first we find the median of the data set.

13, 14, 15, 18, 19, 19, 19, 20

Median = (18 + 19)/2 = 18.5

\(Q_{2}\) = 18.5

Now we calculate the median of first half of the data set to find \(Q_{1}\)

13, 14, 15, 18

\(Q_{1}\) = (14 + 15)/2 = 14.5

and then calculate the median of second half of the data set to find \(Q_{3}\)

19, 19, 19, 20

\(Q_{3}\) = (19 + 19)/2 = 19

IQR = \(Q_{3}\) - \(Q_{1}\)

IQR = 19 - 14.5 = 4.5

Range = 7

IQR = 4.5