Download Standard Deviation

Standard Deviation
Formula
1. Compute the mean for the data set.
2. Compute the deviation by
subtracting the mean from each
value.
3.Square each individual deviation.
4. Add up the squared deviations.
5. Divide by one less than the sample
size.
6. Take the square root.
Definition
• a statistic that tells you how tightly
all the various examples are
clustered around the mean in a set of
data.
• The “average of the averages”
What the Graph Means
Red: 1 Standard Deviation
68% of the data 34% +34%
Red and Green: 95% of the data
Red, Green, Blue: over 98%
68% of data is grouped
near the mean
68% of data
points are
further from
mean
What Does It All Mean?
• large standard deviation indicates that
the data points are far from the mean
• small standard deviation indicates that
they are clustered closely around the
mean.
• Used to determine if the calculated
mean is a valid representation of the
data
Sample Data
Data Points: 73, 58, 67, 93, 33, 18, 147
Mean: 69.9
(73-69.9)2 = (3.1)2 = 9.61
(58-(69.9)2 = (-11.9)2 = 141.61
(67-69.9)2 = (-2.9)2 = 8.41
(93-69.9)2 = (23.1)2 = 533.61
(33-69.9)2 = (-36.9)2 = 1361.61
(18-69.9)2 = (-51.9)2 = 2693.61
(147-69.9)2 = (77.1)2 = 5944.41
Sum: 10,692.87.
Divide by 6 to get 1782.15.
Take the square root of this value to
get the standard deviation, 42.2.