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ANALYZING STATISTICS AND DATA PREP FOR THE AP EXAM
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Standard Deviation and Error Bars

For a detailed explanation of how to calculate standard deviation and standard error of the mean, and a
discussion of error bars, see “Tutorial 1: Statistics” on page 20 . For reference, here are the equations for
) .
standard deviation ( s ) and standard error of the mean (SE x
x
∑∑ ( x i −− ) 2 s
S == SE x ==
n −− 1 n
PRACTICE THE SKILL
Plants capture energy from the environment and trans- Seedling Seedling
form it into chemical energy in the form of organic height (mm) height (mm)
molecules called sugars. They use these sugars for Petri Dishes in dark in light
growth and reproduction. Sunlight is the major source 1 and 2 12 18
of energy for plants. A lack of sunlight prevents plants
from growing well. Researchers performed an exper- 3 and 4 8 22
iment to demonstrate the effect of light on plant 5 and 6 15 17
growth. The researchers grew crofton weed seedlings, 7 and 8 13 23
which are germinated seeds, in 20 petri dishes. Ten
petri dishes remained in the dark and 10 petri dishes 9 and 10 6 16
were exposed to light. The researchers measured 11 and 12 4 18
seedling growth in millimeters over 1 week. The data 13 and 14 13 22
are shown in the table.

1. What is the mean height ()x of the seedlings 15 and 16 14 12

grown in the dark, and the mean height ()x of the 17 and 18 5 19

seedlings grown in the light?
19 and 20 6 17
To calculate the mean of the heights of the seed- Data from https://www.biointeractive.org/sites/default/
lings grown in the dark, we add all of the values fi les/media/fi le/2019-05/Statistics- Teacher- Guide.pdf
in the Dark column and divide by the number of
values in that dataset, which is 10:
12 mm ++ 8mm ++ 15mm ++ 13mm ++ 6 mm ++ 4mm ++ 13mm ++ 14mm ++ 5 mm ++ 6mm == 96mm
96 mm
== 9.6mm
10
We do the same calculation for the values in the Light column:
18 mm ++ 22 mm ++ 17 mm ++ 23 mm ++ 16 mm ++ 18 mm ++ 22 mm ++ 12 mm ++ 19 mm ++ 17 mm == 184 mm
184 mm
== 18.4mm
10
The mean height of the seedlings grown in the dark is 9.6 mm, and the mean height of the seedlings
grown in the light is 18.4 mm.

2. Calculate the standard deviation of the heights of the seedlings grown in the dark and the light.

We know each individual measurement in the dataset ()x i , the mean ()x , and the sample size ( n ) for the

dark and light treatments and can plug this information into the standard deviation formula:
Dark:
x
∑∑ ( x i −− ) 2
s ==
n −− 1
▼

28 UNIT 1 CHEMISTRY OF LIFE

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