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60 UNIT 1 Exploring One-Variable Data

EXAMPLE More chips please Skill 2.C
Measuring variability: The interquartile range (IQR)

PROBLEM: Here again are the data on the percent air in a sample of 14 bags of chips.
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Brand Percent air Brand Percent air
Cape Cod 46 Popchips 45
Cheetos 59 Pringles 28
Doritos 48 Ruffles 50
Fritos 19 Stacy’s Pita Chips 50
Kettle Brand 47 Sun Chips 41
Lays 41 Terra 49
Lays Baked 39 Tostitos Scoops 34
Find the interquartile range.

SOLUTION:
Sort the data values left to right
19 28 34 39 41 41 45 46 47 48 49 50 50 59 from smallest to largest and find the

Median = 45.5 median.
,

19 28 34 39 41 41 45 46 47 48 49 50 50 59 Find the first quartile Q 1 which is the
median of the data values to the left

=Q 1 39 Median = 45.5 of the median in the ordered list.
19 28 34 39 41 41 45 46 47 48 49 50 50 59 Find the third quartile Q 3 which is the
,

median of the data values to the right

=Q 1 39 Median = 45.5 Q = 49 of the median in the ordered list.

3
IQR = 49 − 39 = 10% air
IQR =Q 3 −Q 1
FoR PRAcTIce, TRY eXeRcISe 19

How should we interpret the interquartile range from the example, IQR = 10%
air? The middle half of the distribution of percent air in these 14 bags of chips
has a range of 10%.
The quartiles and the interquartile range are resistant because they are not

affected by a few extreme values. For the air in chips data, Q would still be 49
3
and the IQR would still be 10 if the maximum were 69 rather than 59.
Be sure to leave out the median when you locate the quartiles. In the preceding
example, the median was not one of the data values. For the earlier Close Friends
example data set, we ignore the circled median of 3 when finding Q and Q .

1
3
1 2 2 2 3 3 3 3 4 4 6
Q Median Q 3

1
choosing Summary Statistics
Which measure of center and variability should we use to summarize the distri-
bution of a quantitative variable? That depends on the shape of the distribution

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