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SecTIoN 1D Describing Quantitative Data with Numbers 55

Refer to the parallel dotplots of the length of PVC pipe from the two suppliers

in Figure 1.11 . For Supplier A, the range of the distribution is 601.5 − 598.5 =

3.0 mm. That’s quite a bit smaller than the range of Supplier B’s distribution:
604.0 − 596.0 = 8.0 mm.

Note that the range of a data set is a single number. In everyday language,
caution
people sometimes say things like “The data values range from 17 to 308.” Be sure
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to use the term range correctly, now that you know its statistical definition.
EXAMPLE More chips please Skill 2.C
Measuring variability: The range

PROBLEM: Here are the data on percent air in the 14 bags of chips

from the preceding two examples, along with a dotplot:
Brand Percent air Brand Percent air
Cape Cod 46 Popchips 45 PackStock/Alamy Stock Photo
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
10 20 30 40 50 60
Lays Baked 39 Tostitos Scoops 34 Percent air

Find the range of the distribution.

SOLUTION:
range = 59 − 19 = 40% air range = maximum − minimum
FoR PRAcTIce, TRY eXeRcISe 11

The range is not a resistant measure of variability. It depends on only the maxi-
mum and minimum values, which may be outliers. Look again at the data on the
percent air in bags of chips. Without the possible outlier at 19%, the range of the

distribution would decrease from 40% air to 59% − 28% = 31% air.

The following graph illustrates another problem with using the range as a
measure of variability. Many older movies were recorded on high-resolution film
with a width of 70 mm, much larger than the standard 35-mm film used for mod-
ern movies. The parallel dotplots show the widths (in millimeters) of a sample
68
of 11 strips of 70-mm movie film produced by each of two machines. Both dis-

tributions are symmetric, centered at 70 mm, and have a range of 70.2 − 69.8 =
0.4 mm. But the widths of the film strips made by Machine B clearly vary more
from the center of 70 mm than the film strips made by Machine A.
Machine A

B
69.8 69.9 70.0 70.1 70.2
Film strip width (mm)

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