Download Topic One - science-jess

Statistical Analysis
Variability of data
 All living things vary, even two peas in the same pod,
so how do we measure this variation?
 We plot data usually using the mean, but error bars are
a graphical representation of variability of data.
Error bars show;
either showing range (highest & lowest value)
or showing standard deviation (±1 s.d.)
What is the importance of error bars?
 The error bars show the spread of data around the
mean
 If the error bars are large then the data has a large
range and if they are small the range is smaller.
 If we use the sd as our error bars it is more accurate as
it includes all data and not just the range, which may
be extreme and not representative of the results
1.1.2 Calculate mean and standard deviation of a set of values
 Appreciate the nature of the mean (average) value
 Consider whether mode (most frequent value) or
median values (middle value) would be more
useful.
 12
14 11
15 17 10 13 14
 12
12 12
12 19 122 147 209 12 22
14 16
 10 11 12 13 14 15 16 17 18 19 20
A normal distribution has the same value for mean, median and mode
What is important about normally distributed data?
 Mean is useful, it is the focus of the data
 We can then measure the deviation or variance
from the mean
 Evaluation of the variance of the mean useful
If the data is tightly
clustered there will be
small variances, but if the
data is more evenly
spread over the whole
range, the variance would
be bigger
Standard Deviation
 The standard deviation is an 'average' number for the
distance of the majority of measures from the mean.
 The standard deviation is usually a preferable method of
measuring spread, as opposed to the simpler 'Range'
calculation, as it takes account of all measurements.
 The Greek letter, sigma, (s) is often used to signify standard
deviation.It is of particular value when used with the Normal
distribution, where known proportions of the measurements
fall within one, two and three standard deviations of the
mean.
This shows the standard deviations about a normal distribution
1.1.3 State-standard deviation summarizes the spread of
values around the means and 68% of the values fall
within one standard deviation and 95% of values fall
within two standard deviations
 Mean =66.6
 Standard deviation= 6.6
 Then you can state that if your data is normally
distributed;
 68% of values will fall between 60.0 and 73.2
 95% of values will fall between 53.4 and 79.8
REMEMBER THIS……
 STANDARD DEVIATION summarises the SPREAD of
data around the mean
 68% of all values fall within 1 sd of the mean ( 34%
above and 34% below)
Hand
span
mm±1
120-129
Number of
students
(f)
2
 Visit
www.mymaths.co.uk
130-139
4
140-149
5
 Click on GCSE
statistics - then
standard deviation
150-159
9
160-169
6
170-179
2
180-189
1
 username: west
 password: data
 Calculate mean and
standard deviation
from frequency table
How can we show the S.D. in our
results?
 If we plot the mean, we can then use 1 S.D. on an error
bar to show the amount of spread of data.
 This will indicate how accurate the results are.
 Small error bars = accurate results
 Assume these
bars were for ±1
s.d.
 Comment on
significance