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ANALYZING STATISTICS AND DATA PREP FOR THE AP EXAM
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Averages We divide this sum by the number of values in the dataset, which
in this case is 8:
For a detailed explanation of how to calculate mean, median, and
mode, see page 20 for “Tutorial 1: Statistics.” Here we review how 82 ï 8 = 10.25
to apply the concepts of mean, median, and mode and offer a
problem for you to try. So, the mean is 10.25.
PRACtiCE tHE SKiLL We can also do this calculation using the following equation,

Below is a table listing several different ant species and the where x is the mean, n is the number of values in the dataset,
n
number of queens commonly found in a colony of each and ∑x i is the sum of all of the values in the dataset:

species. Considering the entire dataset, which measurement = i 1
of the number of queens is largest: the mean, median, or 1 n
mode? ==x ∑ x i
n == i 1
1 8
++
Ant species Number of queens x == 8 ∑ (1 30 ++ 5 ++ 12 ++ 2 ++ 20 ++ 5 ++ 7)
in a small colony i ==1
1
Carpenter ant ( Camponotus 1 ==x (82) == 10.25
pennsylvanicus ) 8
Red imported fi re ant ( Solenopsis invicta ) 30 We can find the median and mode by placing the values in
numerical order:
Pavement ant ( Tetramorium caespitum ) 5
Crazy ant ( Paratrechina longicornus ) 12 1, 2, 5, 5, 7, 12, 20, 30
Pharaoh ant ( Monomorium pharaonis ) 2 The median is the midpoint of this dataset of eight values. Because
Ghost ant ( Tapinoma melanocephalum ) 20 we have an even number of values, the median is the mean of the
two middle values, 5 and 7.
Little black ant ( Monomorium minimum ) 5
Argentine ant ( Linepithema humile ) 7 5 + 7 = 12
12 ï 2 = 6
Data from https://www.environmentalscience.bayer.us/-/media/prfunitedstates
/documents/resource-library/product-guide/ant-id-guide.ashx So, the median is 6.

To determine which number is the largest of all of the measure- We can now find the mode. The mode is the most frequent value in
ments, we’ll have to calculate the mean, median, and mode. Let’s a dataset. If we look at the number of queens, we can see that the
begin by calculating the mean of the dataset. In order to do this, number 5 appears twice, more than any other value. So, the mode is 5.
we add together all of the values in the dataset and divide the
sum by the number of values in the dataset. The sum of the The mean is 10.3, the median is 6, and the mode is 5. The largest
values is: of the three values in this case is the mean. Each of these numbers
describes the dataset in a different way, which is described in
1 + 30 + 5 + 12 + 2 + 20 + 5 + 7 = 82 “Tutorial 1: Statistics.”

Your Turn Bean seedling plant Seedling height (cm)
A researcher has planted bean seedlings under different light, 1 20
moisture, and nutrient conditions and monitored their growth over 2 6
several weeks. The data are recorded in the table. What are the
mean, median, and mode for seedling height? 3 15
4 23
5 5
6 15
7 21

12 Unit 1 chemIstry of LIfe

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