Measures of Spread

Measures of Spread
The measures of central tendency can tell us
about central values of data, however we also
want to know how the data clusters around these
Measures of spread (dispersion) – quantities
that indicate how closely the data clusters
around the center. There are different measures
of spread.
Standard Deviation and variance
Population s.d. = 𝑥 − 𝜇
Sample s.d. = 𝑥 − 𝑥𝑏𝑎𝑟
A deviation is the difference between an
individual value in a set of data and the mean
for the data.
The larger the size of the deviations, the greater
the spread of data.
Variance  is the square of the standard
How much variability there is in the data.
If we are working with grouped data, we have to
use data points using a midpoint of the intervals
– similar to the mean of intervals
Quartiles  divide the set of ordered data into
four groups with equal numbers of values;
similar to a median that divides the data into
two equal groups. There are three dividing lines
in order to get quartiles.
Q2 is known as the median. Q1 and Q3 are
the medians of the upper and lower halves of
the data.
Interquartile range  the range of the middle
half of the data (does not necessarily fall in the
middle of the spectrum). The larger the range,
the greater the spread of the central half of the
data. This provides a good measure of spread.
Semi interquartile range  is ½ of the
interquartile range. This tells us how closely
the data clusters around the median.
Box and wisker plot  a way to illustrate the
above mentioned.
Pg 148 # 1,2,3,4,7,8,10,11,14