Download Biostatistics Practice Problem

Biostatistics Practice Problem
The mean, median and mode are types of average.
The range gives a measure of the spread of a set of data.
This section revises how to calculate these measures for a simple set of data.
It then goes on to look at how the measures can be calculated for a table of data.
Calculating the Mean, Median, Mode and Range for simple data
The table below shows how to calculate the mean, median, mode and range for two sets of
data.
Set A contains the numbers 2, 2, 3, 5, 5, 7, 8 and Set B contains the numbers 2, 3, 3, 4, 6, 7.
Measure
The Mean
To find the mean, you
need to add up all the
data, and then divide
this total by the number
of values in the data.
The Median
To find the median, you
need to put the values
in order, then find the
middle value. If there are
two values in the middle
then you find the mean
of these two values.
Set A
2, 2, 3, 5, 5, 7, 8
Set B
2, 3, 3, 4, 6, 7
Adding the numbers up gives:
2 + 2 + 3 + 5 + 5 + 7 + 8 = 32
Adding the numbers up gives:
2 + 3 + 3 + 4 + 6 + 7 = 25
There are 7 values, so you divide
the total by 7: 32 ÷ 7 = 4.57...
There are 6 values, so you divide
the total by 6: 25 ÷ 6 = 4.166...
So the mean is 4.57 (2 d.p.)
So the mean is 4.17 (2 d.p.)
The numbers in order:
2 , 2 , 3 , (5) , 5 , 7 , 8
The numbers in order:
2 , 3 , (3 , 4) , 6 , 7
The middle value is marked in
brackets, and it is 5.
This time there are two values in
the middle. They have been put
in brackets. The median is found
by calculating the mean of these
two values: (3 + 4) ÷ 2 = 3.5
So the median is 5
So the median is 3.5
The Mode
The mode is the value
which appears the most
often in the data. It is
possible to have more
than one mode if there
is more than one value
which appears the most.
The Range
The data values:
2,2,3,5,5,7,8
The data values:
2,3,3,4,6,7
The values which appear most
often are 2 and 5. They both
appear more time than any
of the other data values.
This time there is only one value
which appears most often - the
number 3. It appears more times
than any of the other data values.
So the modes are 2 and 5
So the mode is 3
The data values:
The data values:
To find the range, you
first need to find the
lowest and highest values
in the data. The range is
found by subtracting the
lowest value from the
highest value.
2,2,3,5,5,7,8
2,3,3,4,6,7
The lowest value is 2 and the
highest value is 8. Subtracting
the lowest from the highest
gives: 8 - 2 = 6
The lowest value is 2 and the
highest value is 7. Subtracting
the lowest from the highest
gives: 7 - 2 = 5
So the range is 6
So the range is 5
Resource: http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i5/bk8_5i2.htm
The following data sets are measurements made of the thickness (mm) of shells of the snail Littorina
obtusata found in the rocky intertidal of New England. Snails were collected from sites with crab
predators and without crab predators.
Habitat
With
Crabs
Without
Crabs
Thickness (mm) of shells of the snail Littorina obtusata
1.02
0.88
0.75
0.94
0.81
0.98
0.79
0.83
0.86
0.93
0.91
1.05
0.71
0.78
0.55
0.42
0.61
0.58
0.49
0.33
0.36
0.82
0.62
0.54
Be sure to show all of your work in your lab book.
1. Calculate the mean snail shell thickness with crabs and without crabs.
With crabs: 10.75/12 = 0.90 mm Without crabs: 6.81/12 = 0.57 mm
2. Calculate the range of snail shell thickness with crabs and without crabs.
With crabs: 1.05-0.75 = 0.30 mm Without crabs: 0.82-0.33 = 0.49 mm
3. Calculate the standard deviation of snail shell thickness with crabs and without crabs.
With crabs: 0.09 Without crabs: 0.15
4. Summarize your results in a complete data table.
Mean
Range
Standard deviation
With crabs
0,90
0,30
0,09
Without crabs
0,57
0,49
0,15
5. Which site has snails with thicker shells? Suggest a reason for this finding.
Snails collected from sites with crabs have thicker shells. Because the mean shell thickness is
greater for these snails.
6. For which site is the snails’ shell thickness more variable?
It is more variable in the sites without crabs since their standard deviation is greater.
7. Create a graph depicting the mean, range and standard variation for the data provided.
1
0.9
0.8
0.7
0.6
0.5
With Crabs
0.4
Without Crabs
0.3
0.2
0.1
0
Mean
Range
Standard
deviation
8. Based on your graph, explain whether the shell thickness is significantly different in the two
populations.
Shell thickness is significantly different in the two populations since there is a great
difference in mean and range values between the populations.