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The interquartile range, the range and the mode
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SUMMARY STATISTICS After displaying data using a histogram
or stem plot, we can make even more sense of the data by calculating what are called summary statistics. They give us an idea about:
1. Where the centre of the distribution is 2. How the distribution is spread out.
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5 Summary Statistics Median Interquartile range Range Mode Median (this will be looked at later)
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The Median The median is the midpoint of a set of data. Half the data are less than or equal to the
median We can use the rule : where ‘n’ is
the no. of observations. This will tell us the POSITION of the median.
Eg: 2, 5, 6, 8, 11, 12, 15-How many observations?-Is it in order???
Ans: median = 7 + 8 /2 = 7.5
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TESTING YOUR KNOWLEDGE
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The Interquartile Range This divides a set of data into quarters.
This is referred to as “Quartiles”. The symbols used to refer to these
quartiles are Q1, Q2, Q3. Q2= median The interquartile range IQR= Q3 – Q1 The IQR gives us the range of the
middle 50% of values in a set of data.
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IQR = Q3- Q1• Step 1: Write down the data in ordered form
from lowest to highest• Step 2: Locate the median; that is, locate Q2.• Step 3: Now consider just the lower half of
the set of data. Find the middle score. This score is Q1.
• Step 4: Now consider just the upper half of the set of data. Find the middle score. This score is Q3. The four cases given in the next slide illustrate this method.
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TESTING YOUR KNOWLEDGE
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The range The range of a set of data is the
difference between the highest and lowest values in that set.
You can use the calc: minX and maxX Range= maximum-minimum
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The mode Most occurring/often score. If there is more than one score with the
highest frequency, then all scores with that frequency are the modes.
The mode is a weak measure of the center of data because it may be a value that is close to the extremes of the data.
Look at the previous slide!
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Classwork/Homework Ex 1E pg 22 Q’s 1-8