2.6 Measures of Spread
The Measures of Central Tendency (mean, median and mode) indicate the central values of a set
of data.
Measures of Spread indicate how closely the data cluster around these centres
Quartiles:
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Quartiles divide a set of ordered data into 4 groups with equal numbers of values.
The second quartile (Q2) is the median of the data.
The first quartile (Q1) and the third quartile (Q3) are the medians of the lower and upper
halves of the data.
Interquartile range: Q3 – Q1, this is the range of the middle half of the data. The larger the
range, the larger the spread of the central half of the data
Semi-interquartile range: one half of the interquartile range
Box- and – Whisker Plot:
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The length of the box shows the interquartile range, while the left whisker shows the
range of the data below the first quartile, and the right whisker shows the range above the
third quartile.
Modified box-and-whisker plot is used when the data contains outliers. Any point that is
at least 1.5 times the box length away from the box is classified as an outlier.
Percentiles:
Similar to quartiles, except they divide the data into 100 equal intervals.
See example 5 (pg. 145)
Example 1 Suppose you were to catch and measure the length of 13 fish in a lake:
12, 13, 5, 8, 9, 20, 16, 14, 14, 6, 9, 12, 12
1. Rewrite the data in order, from smallest length to largest:
2. Find the median of all the numbers.
3. Find the lower median and the upper median.
4. Draw an ordinary number line that extends far enough in both directions to include all the
numbers in your data:
5. Locate the main median 12, the lower median 8.5 and the upper median 14 with vertical
lines:
6. Draw a box using the lower and upper median lines as endpoints and the whiskers extend
out to the data`s smallest number 5 and largest number 20:
What information about the data does this graph give you?
The lengths of the fish were as small as 5 cm, and as long as 20 cm. This gives you the range of
the data, 15.
You also know the median, or middle value was 12 cm
Since the medians (three of them) represent the middle points, they split the data into four equal
parts:
Homework: pg. 148 #2-4, 7bc, 8, 14