The table below shows data from a survey about the amount of time high school student spent reading in amount of time spent watching videos each week (without reading). Which response best describes outliers in the data sets?
A. neither data set has suspected outliers
B. The range of data is too small to identify outliers
C. video has a suspected outlier in the 26-hour value
D. due to the narrow range of reading compared to video the video values of 18, 21, and 26 are all possible outliers

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

According to question

Reading:

Median = [tex]\frac{7+12}{2}[/tex] = 9.5

[tex]Q_{1}[/tex] = 5 × 25% + 7 × 75% = 6.5

[tex]Q_{3}[/tex] = 14 × 25% + 12 × 75% = 12.5

IQR is the difference between Q3 and Q1

IQR = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 12.5 - 6.5 = 6

[tex]Q_{1}[/tex] - 1.5 IQR = 6.5 - 1.5 × 6 = -2.5 < Min = 5

[tex]Q_{3}[/tex] + 1.5 IQR = 6.5 + 1.5 × 6 = 15.5 > Max = 15

So no outlier in reading

Video :

[tex]Q_{1}[/tex] = 7 × 75% + 4 × 25% = 6.25

[tex]Q_{3}[/tex] = 21 × 25% + 18 × 75% = 18.75

IQR is the difference between Q3 and Q1.

IQR = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 18.75 - 6.25 = 12.5

[tex]Q_{1}[/tex] - 1.5 IQR = 6.25 - 1.5 × 12.5 = -12.5 < Min = 1

[tex]Q_{3}[/tex] + 1.5 IQR = 18.75 + 1.5 × 12.5 = 37.5 > Max = 26

So no outlier in video

So neither data set has suspected outliers.

Option A is correct.

Find out more information about IQR here

https://brainly.com/question/15448232

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