Math for BiologistsMath for BiologistsSome of the maths skills that are required for IB Biology with examples and practice questions

Calculating Magnification

Practice Questions

A photomicrograph of a tissue is accompanied by a scale bar which represents 1 μm. The scale bar is 10 mm long.

What is the magnification of this photomicrograph?

A.10 X

B.1000 X

C. 10000 X

D. 1000000 X

AnswerA photomicrograph of a tissue is accompanied by a scale bar which represents 1 μm. The scale bar is 10 mm long.

What is the magnification of this photomicrograph?

A.10 X

B.1000 X

C. 10000 X

D. 1000000 X

Practice Question

The width of a human hair is 0.1 mm.

What is the width in μm?

A. 10μm

B. 100μm

C. 1000μm

D. 10000μm

Answer

The width of a human hair is 0.1 mm.

What is the width in μm?

A. 10μm

B. 100μm

C. 1000μm

D. 10000μm

Calculate the Mean

You calculate the mean or average of a set of numbers by adding them all up and dividing by how many numbers you have.

What is the Median?

• The "median" is the "middle" value in the list of numbers.

• To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first.

What Is the Mode?

• The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

Find the mean, median, mode, and range for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

Answer

The mean is the average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

The median is the middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.

Calculate Standard Deviation

• Click on the link for the simplest explanation I have found

• You are not required to calculate s.d. by hand using the formula

• You must be able to do it on a calculator

Statistics Practice QuestionsThe data shows the number of flowers per flower head of a random sample from a white clover (Trifolium repens) population.

36, 51, 56, 62, 62, 63, 65, 69, 73, 83Mean = 62

Standard deviation = 12.5

What statistical percentage of the population has between 49 and 75 flowers per flower head?

A. 5%

B. 32%

C. 68%

D. 95%

Answer

The data shows the number of flowers per flower head of a random sample from a white clover (Trifolium repens) population.

36, 51, 56, 62, 62, 63, 65, 69, 73, 83Mean = 62

Standard deviation = 12.5

What statistical percentage of the population has between 49 and 75 flowers per flower head?

A. 5%

B. 32%

C. 68%

D. 95%

Statistics Question

Which calculation would an ecologist make to examine the spread of values about a mean?

A. Correlation

B.Carrying capacity

C.Lincoln index

D.Standard deviation

Answer

Which calculation would an ecologist make to examine the spread of values about a mean?

A. Correlation

B.Carrying capacity

C.Lincoln index

D.Standard deviation

Practice Question

For the following 10 measurements 4, 5, 5, 6, 6, 6, 6, 7, 7, 8 the mean value is 6. What is the best estimate of the standard deviation?

 

A. 8

B. 6

C. 3

D. 1

AnswerFor the following 10 measurements 4, 5, 5, 6, 6, 6, 6, 7, 7, 8 the mean value is 6. What is the best estimate of the standard deviation?

 

A. 8

B. 6

C. 3

D. 1

Practice QuestionThe average leaf length of one plant is 2.5 cm with a standard deviation of 0.5 cm. What does this indicate?

A.95% of all leaves fall within the ranges of 2.0 to 3.0 cm

B. 68% of all leaves fall within the ranges of 1.5 to 3.5 cm

C. 68% of all leaves fall within the ranges of 2.5 to 3.0 cm

D. 95% of all leaves fall within the ranges of 1.5 to 3.5 cm

AnswerThe average leaf length of one plant is 2.5 cm with a standard deviation of 0.5 cm. What does this indicate?

A.95% of all leaves fall within the ranges of 2.0 to 3.0 cm

B. 68% of all leaves fall within the ranges of 1.5 to 3.5 cm

C. 68% of all leaves fall within the ranges of 2.5 to 3.0 cm

D.95% of all leaves fall within the ranges of 1.5 to 3.5 cm

Using RatiosUsing RatiosWhy?Why?

Used for calculating proportions, e.g. sufferers of Cystic Fibrosis are more frequently female than male, in a ratio of 2:1

Using RatiosUsing RatiosWhy?Why?

Used for calculating proportions, e.g. sufferers of Cystic Fibrosis are more frequently female than male, in a ratio of 2:1. Population size = 200,000

How?How? Step 1: Add the ratio together (x) (2 + 1 = 3)

Step 2: Divide the population size by x (200,000 / 3 = 66666)

Step 3: Multiply by the part of the ratio you are interested in (66666 x 2 = 13,3333)

Percentage IncreasePercentage IncreaseWhy?Why?

Used to calculate the rise of diseases in populations, the effectiveness of medicines… etc… E.g. TB deaths in 1986 = 50,000 and rose to 86,000 in 2003. What is the % increase?

Percentage IncreasePercentage Increase

How?How?Step 1: Find the two values ‘new’ and ‘old’ (86000 and

50000)

Step 2: Find the difference between these two values (86,000 – 50,000 = 36,000)

Step 3: Divide by the ‘old’ value (36000/50000 – 0.72)

Step 4: Multiply by 100 and remember to your units! (0.72 x 100 = 72%)

Percentage Increase Question

Question Continued…

1. State the percentage increase in the risk of developing high blood pressure if the BMI of 33 is compared to the BMI of 22.

1. Identify the percentage increase in risk of death from all causes if the BMI increases from 28 to 33.

Answer

1. 350%

2. 60%

Question Continued…

• Calculate the percentage increase in the risk of dying of cancer, if a patient who is 2 m tall increases in weight from 120 kg to 132 kg. Show your working.

Answer

Calculation of both BMI/BMI=120/4 = 30

and BMI=132/4 = 33;

Percentage DecreasePercentage Decrease

Why?Why?

Used to calculate the effectiveness of a medicine, the decline in disease, loss of white blood cells, red blood cells…etc!

How? How?

Step 1: Find the two values ‘old’ and ‘new’

Step 2: Find the difference between these values

Step 3: Divide by the ‘old’ value

Step 4: Multiply by 100 & remember your units! %

General Math Question

How many peptide bonds are in a polypeptide made of 120 amino acids?

A. 119

B.120

C.359

D. 360

Answer

How many peptide bonds are in a polypeptide made of 120 amino acids?

A. 119

B.120

C.359

D. 360

Genetics Questions

Genetics Questions

Calculate Lincoln Index

• Click on the link for the simplest explanation

• You must understand what the Lincoln Index or Capture Mark Recapture is