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ANALYZING STATISTICS AND DATA PREP FOR THE AP EXAM
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Percent Change PRACtiCE tHE SKiLL
Let’s look at an example of how percent change might be used.
In biology, percentages are frequently used to describe and ana-
lyze data. For example, a researcher might use percentages to James Kirkham Ramsbottom discovered a way to eliminate para-
describe the concentration of a solution, or to compare the num- sites from daffodil bulbs by immersing them in hot water. Before
bers of each gender in a group. he found an effective soaking time of 2 to 4 hours, he immersed
50 bulbs for 30 minutes and 50 bulbs for 1 hour. At the end of
Percentages describe “parts per hundred” or “parts of a whole.” 30 minutes, 10 of the daffodil bulbs were free of parasites. After
For example, imagine you have 10 trees in your yard and 4 of 1 hour, 25 of the bulbs were free of parasites. What was the per-
4

them are maple trees. You could say that or 0.4 of the trees cent change in the number of healthy, parasite-free bulbs as the

10
in your yard are maple trees. However, you can also calculate immersion time increased?
the number of maple trees per 100 trees, or the percentage of
maple trees. To find the percentage of maple trees, you multiply To start, we must find the two values we need to calculate
0.4 by 100: percent change. After 30 minutes, 10 of the 50 bulbs were free
of parasites. The initial value is 10 bulbs. At the end of 1 hour,
0.4 ë 100 = 40% 25 bulbs were free of parasites. So, the final value is 25 bulbs.
Now we can plug these values into our formula:
In other cases, scientists might be interested in calculating percent
change. This is useful to compare an initial value to a final value, %Change == 25 −− 10 ×× 100
which allows you to see how much something has increased or 10
decreased. Use the following formula to calculate percent change: %Change == 15 ×× 100
10
final value - initial value
% change = ë 100 %Change == 1.5 ×× 100
initial value %Change == 150%
If the final value is larger than the initial value, the percent change There was a 150% increase in parasite-free bulbs as Ramsbottom
is a positive number, representing an increase between the values changed the immersion time from 30 minutes to 1 hour.
you are comparing. If the final value is smaller than the initial value,
the percent change is a negative number, signifying a decrease
between the values you are comparing.

Your Turn
The emerald ash borer is an invasive species that has destroyed ash tree populations in North America. Before the insect arrived,
one forest contained 300 ash trees. A number of years after the ash borer was introduced to the area, only 60 ash trees remained.
By what percent did the ash tree population decrease?

or quantitative. Qualitative data are descriptive. For example, also indicate the extent to which the observed measurements
the stem of a corn plant can be described as “short” or “tall.” deviate from the average. The spread of the data can be calcu-
Quantitative data are expressed numerically. For example, lated in various ways, each of which provides an indication of
a corn stem might measure 2.04 m or 2.76 m in length. how tightly the data points are clustered around the average.
Similarly, the heart rate data that we collected in our con- Statistics can also help researchers understand whether
trolled experiment is an example of quantitative data. Scien- the data collected for the experimental and control groups
tists often deal with quantitative data because numbers lend reflect a real, or what is termed a statistically significant,
themselves to statistical analysis. difference. For example, in the caffeine experiment, let’s say
Statistical analysis helps scientists interpret the data they col- we observe that resting heart rate is higher in the test group
lect. For example, when several measurements are made, they compared to the control group. Is this difference the result
are typically not all the same. In this case, the researcher might of caffeine, in which case scientists call it a real difference?
report the average of the measurements. The researcher might Or is the difference just due to chance?

10 Unit 1 chemIstry of LIfe

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