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What do we mean by measure of spread?
What do we mean by measure of spread?
Measure of spread, relates to a statistical calculation which analyses the spread of the data, in other words how far apart the data is. The most common measure of spread used so far is the range. However, the range has its limitations as it can be skewed by outliers, very large or very small data within the data set. Therefore we look into two other measures of spread the interquartile range and standard deviation.
Range
Range
= maximum - minimum
Quartiles
Quartiles
We all know how to find the median of a data set, which is the central value which splits a data set in half. Quartiles are similar but split the data set into 4 equal parts, or quarters. These are called Q1 (Lower Quartile), Q2 (median) and Q3 (Upper Quartile).
To find the quartiles of a data set:
To find the quartiles of a data set:
Step 1: Order the data from smallest to largest.
Step 2: Find the median and call it Q2.
Step 3: Find the middle of the bottom set of data up to the median, call it Q1.
Step 4: Find the middle of the top set of data from the median, call it Q3.
Examples
Examples
Find the quartiles for each data set:
a) 2 3 4 6 6 7 8 8 9 10
b) 15 18 7 16 23 9 15 20 16 14 13 11 19
c) 65 84 75 82 97 70 68 76 93 48 79 54 80 79 82 96 63 85 72 70
Answers
Answers
a) Q1 = 4, Q2= 7 and Q3=9
b) Q1 = 12, Q2= 15 and Q3= 18.5
c) Q1 = 69, Q2 = 77.5 and Q3 = 83
The Interquartile Range
The Interquartile Range
The interquartile range is another measure of spread that is calculated by the difference between the upper and lower quartile. The interquartile range encompasses the middle 50% of the data.
IQR = Q3-Q1
Can you find the IQR for each of the data sets above?
Explore
Explore
Explore and investigate interquartile range using the GeoGebra applet below.
Practice
Practice
We may also be asked to calculate quartiles from dot plots and stem and leaf diagrams.
Technology
Technology
Watch the video to see how you can find the quartiles and interquartile range in google sheets.
Interdisciplinary Component
Interdisciplinary Component
With your data from before can you also find the quartiles and interquartile range for the different fitness tests.
What can you deduce from this information? This will help you later on when it comes to drawing box plots.
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