Question

The table below shows data from a survey about the amount of time students spend doing homework each week. The students were in either college or high school:HighLowQ1Q3IQRMedianMeanσCollege206818101413.35.2High School2035.51610.511115.4Which of the choices below best describes how to measure the spread of these data?(Hint: Use the minimum and maximum values to check for outliers.) Both spreads are best described by the IQR. Both spreads are best described by the standard deviation. The college spread is best described by the IQR. The high school spread is best described by the standard deviation. The college spread is best described by the standard deviation. The high school spread is best described by the IQR.Can you please help me understand how to solve this problem?

Answer 1

Firstly, let us check for the outliers as instructed in the question

For college,

Q3 = 18

Q1=8

IQR = 10

maximum = 20

minimum = 6

For there to be outliers, The maximum must be greater than Q3 + 1.5(IQR) or the minimum must be less than Q1 -1.5(IQR)

Q3 + 1.5(IQR) = 8 + 1.5(10) = 23

Q1 -1.5(IQR) = 6 - 1.5(10) = -9

The maximum (20) is not greater than 23 and the minimum (6) is not less than -9. Hence we can conclude that college data has no outlier

For High school,

Q3 = 16

Q1= 5.5

IQR = 10.5

maximum = 20

minimum = 3

Q3 + 1.5(IQR) = 16 + 1.5(10.5) = 31.75

Q1 -1.5(IQR) = 5.5 - 1.5(10.5) = -10.25

The maximum (20) is not greater than 31.75 and the minimum (3) is not less than -10.25. Hence we can conclude that High school data has no outlier

Since both spreads have no outliers, The best way to describe the spreads is by their IQR.

The makes the correct answer to be the first option that is (Both spreads are described by their IQR)