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50 UNIT 1 Exploring One-Variable Data

Brand Percent air Brand Percent air
Cape Cod 46 Popchips 45
Cheetos 59 Pringles 28
Doritos 48 Ruffles 50
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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 median.
SOLUTION:

19 28 34 39 41 41 45 46 47 48 49 50 50 59
Sort the data values from smallest to largest. Because there
45 46 are n = 14 data values (an even number), use the average of
+
The median is = 45.5 % air. the middle two values in the ordered list as the median.
2
FoR PRAcTIce, TRY eXeRcISe 1

Here is a dotplot of the air in chips data from the preceding example with the
median of 45.5 marked. How should we interpret the median? About half of the
chip brands have less than 45.5% air, and about half have more.
Median

10 20 30 40 50 60
Percent air

Measuring center: The Mean

The most commonly used measure of center is the mean.

DEFINITION The mean
The mean of a distribution of quantitative data is the average of all the individual
AP® EXAM TIP data values. To find the mean, add all the values and divide by the total number of
Formula sheet data values.
,
The formula for the sample If the n data values are xx, 2 , … x , the sample mean x (pronounced “x-bar”) is
1
n
mean x is included on the for- given by the formula
mula sheet provided on both sumofdatavalues x + x + …+ x ∑ x
sections of the AP® Statistics x = numberofdatavalues = 1 2 n n = n i
exam.

The ∑ (capital Greek letter sigma) in the formula is short for “add them all
up.” The subscripts on the observations x are just a way of keeping the n data val-
i
ues distinct. They do not necessarily indicate the order or any other special facts
about the data.

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