Transcript Maths for Biologists

Math for Biologists
Some 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
Answer
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
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 Questions
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, 83
Mean = 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, 83
Mean = 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.
B.
C.
D.
8
6
3
1
Answer
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.
B.
C.
D.
8
6
3
1
Practice Question
The 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
Answer
The 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 Ratios
Why?
Used for calculating proportions, e.g.
sufferers of Cystic Fibrosis are more
frequently female than male, in a ratio of 2:1
Using Ratios
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?
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 Increase
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 Increase
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 Decrease
Why?
Used to calculate the effectiveness of a
medicine, the decline in disease, loss of white
blood cells, red blood cells…etc!
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
14.
In the pedigree shown below, the female, labelled I-2, is a carrier for colour blindness, however
neither male (I-1 or II-1) is colour blind.
I
1
2
2
3
II
1
III
offspring
1
What is the probability that of fspring III-1 will be colour blind?
A.
50 %
B.
25 %
C.
12.5 %
D.
0%
Calculate Lincoln Index
• Click on the link for the simplest
explanation
• You must understand what the Lincoln
Index or Capture Mark Recapture is