Transcript Measures of Spread

Measures of Spread
 Spread, dispersion and variation all refer to
a measure of the way a data set is distributed
around a central value.
Ways to Measure Spread
1. Range: the difference between the max and
min values.
2. Quartiles: The 3 median values that divide
the data into 4 equal parts.
3. Interquartile Range: the difference between
the first and third quartiles. Contains the
middle 50% of the data.
4. Variance: measure of dispersion that is
found by averaging the squares of the
deviation (distance from the mean) of each
piece of data
Calculating Variance:
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2
x  x

n

2
5.
Standard Deviation: the square root of the
variance
Calculation:
x  x
 
n

2
What do these measures tell us about
the data?
 Quartiles and Interquartile Range:
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tell us how spread out the middle 50% of the
data is
Helps in constructing a box plot
 Variance:
 how the elements are spread around the mean.
 large variance means the data is widely spread
around the mean.
 Standard Deviation:
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The standard deviation is in the same 'scale'
as the mean is. The makes these two
indicators 'comparable'.
how the elements are spread around the
mean.
large variance means the data is widely
spread around the mean.