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spread. So we calculate range as:
spread. So we calculate range as:
Range = maximum value - minimum value
Range = maximum value - minimum value
For example, let us consider the following data
For example, let us consider the following data
23 56 45 65 59 55 62 54 85 25
23 56 45 65 59 55 62 54 85 25
The maximum value is 85 and the minimum value is
The maximum value is 85 and the minimum value is
23. This results in a range of 62, which is 85 minus 23. Whilst using
23. This results in a range of 62, which is 85 minus 23. Whilst using
your study and your range is 7 to 123 years old you know you have
your study and your range is 7 to 123 years old you know you have
made a mistake!
made a mistake!
Quartiles tell us about the spread of a data set
Quartiles tell us about the spread of a data set
by breaking the data set into quarters, just like the median breaks
by breaking the data set into quarters, just like the median breaks
below, which have been ordered from the lowest to the highest scores,
below, which have been ordered from the lowest to the highest scores,
and the quartiles highlighted in red.
and the quartiles highlighted in red.
20th 42 40th 52 60th 64 80th 74 100th 85
20th 42 40th 52 60th 64 80th 74 100th 85
and 76th student's marks. Hence:
and 76th student's marks. Hence:
First quartile (Q1) = 45 + 45 ÷ 2 = 45
First quartile (Q1) = 45 + 45 ÷ 2 = 45
Third quartile (Q3) = 71 + 71 ÷ 2 = 71
Third quartile (Q3) = 71 + 71 ÷ 2 = 71
In the above example, we have an even number of
In the above example, we have an even number of
scores (100 students rather than an odd number such as 99 students).
scores (100 students rather than an odd number such as 99 students).
recognize that the second quartile is also the median.
recognize that the second quartile is also the median.
Quartiles are a useful measure of spread because
Quartiles are a useful measure of spread because
they are much less affected by outliers or a skewed data set than the
they are much less affected by outliers or a skewed data set than the
the scores in the distribution. Hence, for our 100 students:
the scores in the distribution. Hence, for our 100 students:
Interquartile range = Q3 - Q1
Interquartile range = Q3 - Q1
= 26
= 26
However, it should be noted that in journals and
However, it should be noted that in journals and
other publications you will usually see the interquartile range
other publications you will usually see the interquartile range
reported as 45 to 71, rather than the calculated range.
reported as 45 to 71, rather than the calculated range.
A slight variation on this is the
A slight variation on this is the
semi-interquartile range, which is half the interquartile range = ½
semi-interquartile range, which is half the interquartile range = ½
(Q3 - Q1). Hence, for our 100 students, this would be 26 ÷ 2 = 13.
(Q3 - Q1). Hence, for our 100 students, this would be 26 ÷ 2 = 13.
== Standard Deviation ==
== Standard Deviation ==
