,
for a sample:
5.6 Measures of Spread
Ex 1 The table shows the heights of players on two basketball teams
|
Falcons |
Ravens |
|
183 165 148 146 181 178 154 |
166 163 168 161 165 166 166 |
Which team has the height advantage?
The measures of central tendency don't tell you enough about the data to make a concrete judgment. They don't tell you how the data is dispersed.
The Standard Deviation is a tool used to measure how data is spread about the mean.
The standard deviation has slightly different formulas depending on whether you're discussing a population or a sample.
For
a population:
,
for a sample:
notice:
different denominators, μ
and
,
σ and s.
The higher the standard deviation, the wider the spread about the mean.
Sometimes the variance is asked for, the variance is the square of the standard deviation.
Population
variance:
,
sample variance:
Ex 2 On a spreadsheet, calculate the mean, standard deviation and variance for the findings on the lifespans of a rare breed of cat.
16, 18, 19, 12, 11, 15, 20, 21, 18, 15, 16, 13, 16, 22, 18, 19, 17, 14, 9, 14, 15, 19, 20, 15, 15
Z-scores
– the number of standard deviations a data entry is from the
mean. A negative z-score means a data point is below the mean. The
formula is
or
,
depending on context.
Ex 2b What would the z-score be for a cat aged 19 years?
p. 148# 1, 5, 6a, 7a, 9a, 10