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10.6 Representing variation
graphically
Calculation teacher sheet
OCR Biology A
Standard deviation
Specification reference

4.2.2

Maths skill 1.10
Learning outcomes
After completing this worksheet students should be able to:

calculate standard deviation using a formula

relate the calculated values of standard deviation to error bars on graphs

compare means of data.
Introduction
This sheet is designed to allow students to practise calculating standard deviation (SD) by hand.
It also aims to help them to understand how the SD is used to compare means and derive error
bars for graphs.
Teacher notes

Students should understand that a successful SD calculation will have little meaning unless
there are sufficient repetitions, which means at least 5.

The example deliberately includes an outlier so that the resulting error bar can be compared
with the range bar. This is to try and clarify that SD can be a better tool than a range bar in
such situations so that an outlier has less effect (assuming it is included).

Students should be encouraged to use SD routinely. To save time they can be shown how to
use the Excel spreadsheet function. This is STDEV(C1:C12), where the bracketed numbers
describe which cells to include. These can be selected quickly by holding down the left
mouse button and dragging across the cells to include. In this example, cells 1–12 in column
C have been selected.
Students will not be asked to calculate SD in a written paper.

Maths skills links to other areas
Whenever students collect data they should consider using standard deviation to test the
dispersion of the results and add error bars to their graphs as a normal part of their processing.
To save time they can use spreadsheets to find SD automatically.
Answers
1
a
b
c
The mean values for five temperatures rows are 3.6, 13.6, 20.8, 20.0, and 32.8 (one
mark deducted per error. Values must have same decimal places as the original data).
One mark for each correct value:
The SD values are 1.9, 1.3, 3.1, 7.5, 5.0.
Any two from:
The mean, at 5 °C is the most reliable/at 15 °C is the least reliable.
Because SD is smallest at 5 °C/ largest at 15 °C.
Data at 5 °C are less spread/have less variation/are less dispersed from the mean/ORA.
© Oxford University Press 2015
(3 marks)
(5 marks)
(1 mark)
(1 mark)
(1 mark)
www.oxfordsecondary.co.uk/acknowledgements
This resource sheet may have been changed from the original
1
10.6 Representing variation
graphically
Calculation teacher sheet
OCR Biology A
2
3
The limits are 14.9 and 12.3 (one mark for each correct limit).
a One mark for each correct answer:
The means for the students from 1 to 5 are 15.3, 22.8, 22.8, 22.8, 22.8.
b One mark for each correct answer:
The SD for the students from 1 to 5 are 7.1, 5.9, 4.3, 2.9, 2.4.
c Any five from:
The true mean is (close to) 22.8;
All students with five or more repetitions succeed in getting an accurate mean
As the number of repeats increases the standard deviation becomes smaller
There is less, spread/dispersion, in the data/outliers have less effect;
Student 1 has insufficient data to calculate an accurate mean
Error bars become smaller as the number of repeats increase
Although the means for students 2–5 are the same, students 4 and 5 have the
most certainty.
Students 4 and 5 will be able to plot the points with the greatest certainty.
There is no significant benefit in repeating this experiment more than eight times.
© Oxford University Press 2015
(2 marks)
(5 marks)
(5 marks)
(max 5 marks)
www.oxfordsecondary.co.uk/acknowledgements
This resource sheet may have been changed from the original
2