Mathematics Grade 10
Lesson Notes
Calculating with Data
7
Lesson
Teacher Guide
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Range and other Measures of Dispersion
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In this lesson, we look at different ways of finding out how
R spread out a set of data is. We find the range,
lower and upper quartiles, and the interquartile and semi-interquartile ranges.
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Lesson Outcomes
Curriculum Links
LO4: Data Handling and Probability.
10.4.1 (a) Collect, organise and interpret data in
order to determine measures of dispersion: range,
percentiles, interquartile and semi-interquartile
range.
By the end of this lesson, you should be able to:
• calculate range
•calculate interquartile range
•calculate semi-interquartile range
•compare data using this information
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Lesson notes
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We have looked at the average as one way of
analysing data. Another aspect of analysing data
is to look at how spread out the data is. A simple
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measure of spread is called the range.
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The
2+2=4 shows the difference between the
E range
smallest and the biggest value in our data set.
For example, let’s consider the masses of twelve
burger patties:
286 g
312 g
286 g
324 g
292 g
356 g
298 g
363 g
Once you have found your quartiles, you can
find the interquartile range. This is the range of
numbers between the lower and upper quartiles.
In this case, the interquartile range will be 51 g
(340 – 289 = 51). In some situations this value is
more useful than the range, because it shows us
the spread without the extreme measurements.
300 g
401 g
The biggest value in this data set is 401, and the
smallest is 251. This means that our range is
150 g.
This shows that our data is very spread out,
because we would expect all the patties to have
a similar mass. You may have noticed that most
of the masses are much closer to 300 grams. 251
grams is extremely low in comparison, and 401
grams is extremely high in comparison.
Another way of analysing the spread of data,
without the results being affected by extreme
measurements, is to divide our data set into
quartiles, or four parts. This means dividing our
data into four parts. We halve our data to find the
median, and then we divide each half of the data
into two parts again.
This information can be shown on a box-andwhisker plot.
Sometimes researchers divide the interquartile
range into half again. This is called the semiinterquartile range. For example,
51 ÷ 2 = 25,5 g. This gives an even smaller range
within the middle part of the data.
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251g
300 g
The median lies between the sixth and the
seventh value, so it is 300 g.
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Halfway between 286 and 292 is 289 g. We call
this the lower quartile.
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Halfway between 324 and 356 is 340 g. This is
called the upper quartile.
2+2=4
? Task
Find the range, the interquartile range and the
semi-interquartile range for this data:
8kg 8kg 7kg 9kg 8kg 9kg 2kg 1kg 1kg 2+2=4
2kg 4kg 5kg 4kg