Comparing range and interquartile range (IQR)

Range and interquartile range (IQR) both measure the "spread" in a data set. Looking at spread lets us see how much data varies. Range is a quick way to get an idea of spread. It takes longer to find the IQR, but it sometimes gives us more useful information about spread.

Part 1: The range

Ron recorded the daily high temperatures for two different cities in a recent week in degree Celsius. The temperatures for each city are shown below.

Kansas City, MO:

23, 25, 28, 28, 32, 33, 35

Paradise, MI:

16, 24, 26, 26, 26, 27, 28

problem a

Calculate the range of the temperatures in Kansas City, MO.

range =

problem b

Calculate the range of the temperatures in Paradise, MI.

range =

problem c

What is the best interpretation of the range?

(Επιλογή Α)
The range represents the typical temperature that week.
(Επιλογή Β)
The range represents how far apart the lowest and the highest measurements were that week.
(Επιλογή Γ)
The range represents the amount of spread in the middle half of the data that week.

problem d

According to the ranges, which city's temperatures were more varied in that week?

(Επιλογή Α)
According to the ranges, the temperatures varied more in Paradise, MI.
(Επιλογή Β)
According to the ranges, the temperatures varied more in Kansas City, MO.
(Επιλογή Γ)
According to the ranges, the temperatures in each city had the same amount of variability.

Part 2: The interquartile range (IQR)

problem a

Calculate the IQR of the temperatures in Kansas City, MO.
As a reminder, here are the temperatures:

23, 25, 28, 28, 32, 33, 35

IQR =

problem b

Calculate the IQR of the temperatures in Paradise, MI.
As a reminder, here are the temperatures:

16, 24, 26, 26, 26, 27, 28

IQR =

problem c

What is the best interpretation of the IQR?

(Επιλογή Α)
The IQR represents the typical temperature that week.
(Επιλογή Β)
The IQR represents how far apart the lowest and the highest measurements were that week.
(Επιλογή Γ)
The IQR approximates the amount of spread in the middle half of the data that week.

problem d

According to the IQRs, which city's temperatures were more varied in that week?

(Επιλογή Α)
According to the IQRs, the temperatures varied more in Paradise, MI.
(Επιλογή Β)
According to the IQRs, the temperatures varied more in Kansas City, MO.
(Επιλογή Γ)
According to the IQRs, the temperatures in each city had the same amount of variability.

Part 3: Comparing range and IQR

Ron made a dot plot for the temperatures in each city.

problem a

Looking at the dot plots, which city's temperatures seem to be more varied from day to day?

(Επιλογή Α)
Temperatures in Kansas City, MO seemed to vary more from day to day, because individual dots are more spread out from each other.
(Επιλογή Β)
Temperatures in Paradise, MI seemed to vary more from day to day because individual dots are clustered closer together.

problem b

Why might IQR be the preferred measure of spread in this context?

(Επιλογή Α)
The low outlier in the Paradise temperatures has a large impact on the range of that data set, while IQR is not impacted by the outlier.
(Επιλογή Β)
The IQR was larger in the Kansas City data, which reflects how the temperatures generally seemed to vary more from day to day in Kansas City than they did in Paradise.
(Επιλογή Γ)
The range shows that the data is more clustered in Paradise.

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