Statistics in

Biology: Standard Deviation &

Standard Error

AP Biology

Bloomington High School

Standard Deviation

Measure of how spread out the data is

from the mean

Standard Deviation

Lower standard deviation

Data closer to the mean

More likely the independent variable is

causing the changes in the dependent

variable

Standard Deviation

Higher the standard deviation

Data more spread out from the mean

More likely factors, other than independent

variable, are influencing dependent

variable

Standard Deviation

68% of data fall within

1 of mean

95% within 2 of mean

99% within 3 of mean

Standard Deviation

Calculated value represents location, on the number line, of

1, 2, and 3 standard deviation(s)

68% of data between 45 and 55

95% of data between 40 and 60

68% of data between 40 and 60

95% of data between 30 and 70

68% of data between 50 and 150

95% of data between 0 and 200

68% of data between 90 and 110

95% of data between 80 and 120

Calculating Standard Deviation

1. Calculate the mean

Calculating Standard Deviation

1. Calculate the mean

2. Determine the

differences

Calculating Standard Deviation

1. Calculate the mean

2. Determine the

differences

3. Square the

differences

Calculating Standard Deviation

1. Calculate the mean

2. Determine the

differences

3. Square the

differences

4. Sum the squares

Calculating Standard Deviation

1. Calculate the mean

2. Determine the

differences

3. Square the

differences

4. Sum the squares

5. Divide by sample size

(n) minus 1

Calculating Standard Deviation

1. Calculate the mean

2. Determine the

differences

3. Square the

differences

4. Sum the squares

5. Divide by sample size

(n) minus 1

6. Take the square root

Standard Error

Indication of how well the mean of a

sample estimates the true mean of a

population or whole

Measure of accuracy if the true mean is

known

Measure of precision if true mean is not

known

Low Accuracy

High Precision

High Accuracy

Low Precision

High Accuracy

High Precision

Accuracy is how close a measured value is to the

actual (true) value.

Precision is how close the measured values are to

each other.

Calculating Standard Error

1. Calculate standard

deviation

2. Divide standard

deviation by square

root of sample size

How do we use Standard Error

Create bar graph

Mean on Y-axis

Sample(s) on the

X-axis

Chemical 1 mean

is 30 cm

Chemical 2 mean

is 50 cm

0

10

20

30

40

50

60

Chemical 1 Chemical 2

Len

gth

(c

m)

Root Length

How do we use Standard Error

Add error bars

±SE

Add key that error

bars represent

standard error (SE)

0

10

20

30

40

50

60

70

Chemical 1 Chemical 2

Len

gth

(c

m)

Root Length

Error bars represent standard error

How do we use Standard Error

Look for overlap of

error lines

If overlap –

difference not

significant

If no overlap –

difference

significant

0

10

20

30

40

50

60

70

Chemical 1 Chemical 2

Len

gth

(c

m)

Root Length

Error bars represent standard error

Statements

Fish2Whale food caused the most fish growth

Fish2Whale food caused more fish growth than

did Budget Fude

Statements:

More males in all

four regions

exhibited the trait

measured than did

females.

More males in

region 3 exhibited

the trait measured

than did females

Mean belief scores for misleading ads

vmPFC = damage to ventromedial prefrontal cortex

BDC = brain damaged comparison group

Statements:

1. The vmPFC group identified fewer ads as misleading than did the normal group

2. The BDC group identified more ads as misleading than did the normal group.

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