Transcript Understanding standard deviation File

Standard deviation
• widely used measurement of variability or
diversity used in statistics.
• It shows how much variation or "dispersion"
there is from the "average" (mean, or
expected/budgeted value).
• A low standard deviation indicates that the data
points tend to be very close to the mean,
• whereas high standard deviation indicates that
the data are spread out over a large range of
values.
• Lower case
sigma means
'standard
deviation'.
• Capital sigma
means 'the sum
of'.
• x bar means 'the
mean'
• The standard deviation measures the spread of the
data about the mean value.
• It is useful in comparing sets of data which may have
the same mean but a different range.
• For example, the mean of the following two is the
same:
– 15, 15, 15, 14, 16 and
– 2, 7, 14, 22, 30.
• However, the second is clearly more spread out. If a set
has a low standard deviation, the values are not spread
out too much.
Error bars
• These can be added to line or bar charts to
show the spread of the data around the mean
• If you are asked to plot the error bars of +/one standard deviation above the mean, then
it means that you need to use your calculated
value and plot a vertical line of that value
above (+ value) and below (-value) the mean
For example:
• The error bars shown in the line
graph above represent a
description of how confident
you are that the mean
represents the true impact
energy value.
• The more the original data
values range above and below
the mean, the wider the error
bars and less confident you are
in a particular value.
• Tight distribution of points
around 100 degrees - small error
bars; loose distribution of points
around 0 degrees - large error
bars.
• More precisely, the part of the
error bar above each point
represents plus one standard
error and the part of the bar
below represents minus one
standard error.
You can also add error bars to bar
charts: