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Course: Statistics and probability > Unit 3

Lesson 3: Interquartile range (IQR)
Math
Statistics and probability
Summarizing quantitative data
Interquartile range (IQR)
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Comparing range and interquartile range (IQR)

Google Classroom
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 =
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

problem b
Calculate the range of the temperatures in Paradise, MI.
range =
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

problem c
What is the best interpretation of the range?
صرف 1 جواب چنو

problem d
According to the ranges, which city's temperatures were more varied in that week?
صرف 1 جواب چنو

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 =
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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 =
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

problem c
What is the best interpretation of the IQR?
صرف 1 جواب چنو

problem d
According to the IQRs, which city's temperatures were more varied in that week?
صرف 1 جواب چنو

Part 3: Comparing range and IQR

Ron made a dot plot for the temperatures in each city.
A double dot plot with the upper half modeling the Kansas City, Missouri and the lower half models the Paradise, Michigan. The number line is labeled temperature in degrees celsius. The Kansas City, Missouri dots range from 21 to 35. The Paradise, Michigan dots range from 16 to 28, but there is a cluster of dots from 26 to 28 with only one dot at 16 and a gap from 17 to 23.
problem a
Looking at the dot plots, which city's temperatures seem to be more varied from day to day?
صرف 1 جواب چنو

problem b
Why might IQR be the preferred measure of spread in this context?
Choose all answers that apply: وہ سب سلیکٹ کریں جو مناسب ہے

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