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Ex1E median, the interquartile range, the range and the mode.

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1 Ex1E median, the interquartile range, the range and the mode

2 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.

3 5 Summary Statistics  Median  Interquartile range  Range  Mode  Median (this will be looked at later)

4 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 = /2 = 7.5

5 TESTING YOUR KNOWLEDGE

6 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.

7 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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10 TESTING YOUR KNOWLEDGE

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14 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

15 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!

16 Classwork/Homework  Ex 1E pg 22 Q’s 1-8

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