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Chapter 3: Numerical Descriptive Measures
Some part of chapter 3 has been covered in the lab session of section 2 due to being
behind of the schedule. Thus, that part has been provided here since some students did
not have pen and paper to take notes in the lab.
Quartile Measures
Quartiles split the ranked data into 4 segments with an equal number of
values per segment
The first quartile, Q1, is the value for which 25% of the observations are
smaller and 75% are larger
Q2 is the same as the median (50% of the observations are smaller and
50% are larger)
Only 25% of the observations are greater than the third quartile
Find a quartile by determining the value in the appropriate position in the ranked data:
First quartile position:
Q1 = (n+1)/4
ranked value
Second quartile position:
Q2 = (n+1)/2
ranked value
Third quartile position:
Q3 = 3(n+1)/4
ranked value
, where
n
is the number of observed values
When calculating the ranked position use the following rules:
If the result is a whole number then it is the ranked position to use
If the result is a fractional half (e.g. 2.5, 7.5, 8.5, etc.) then average the
two corresponding data values.
If the result is not a whole number or a fractional half then round the
result to the nearest integer to find the ranked position.
Example:
Sample Data in Ordered Array:
11
12
13
16
16
17
18
21
22
Q1 is in the
(9+1)/4 = 2.5 position of the ranked data, so
Q1 = (12+13)/2 = 12.5
Q1
Q2
Q3
25%
25%
25%
25%
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Q2 is in the
(9+1)/2 = 5th position of the ranked data, so
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 Spring '11
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