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© 2014 Pacific Crest
295
Step
Explanation
2.
Describe the type
of data
Is the data nominal, ordinal, interval or ratio?
Since heights are measured in inches, there is a natural zero and ratios are relevant so
the data has the ratio level of measurement.
3.
Construct a
histogram or bar
graph
Determine if the data has outliers or if it is skewed. Use a histogram for
ratio, or interval data. Use a bar graph for nominal or ordinal data. If some
numbers are drastically different from the great majority of data, the set has
outliers. If the left and right sides are not mirror images and if either tail is
much longer than the other, the data set is skewed
Looking at the histogram, it appears that the data set is symmetric.
4.
Determine which
measures of CT
are reasonable
If the data has the ratio or interval level of measurement, then the mean,
median and mode are relevant.
If the ratio/interval data set is skewed or has outliers, the median is most
reasonable.
If the ratio/interval data is symmetric, the mean is most reasonable
The heights are symmetric and ratio, therefore the mean is most relevant. Since the
data is ratio, it is fair to construct the median and the mode.
5.
Compute the
measures of CT
and determine
which is best
If it is fair to construct the mean, median, or mode do so:
Mean = Sum(var)/Num
Median is the middle value of a sorted set of values if an odd number of
values or the average of two middle values if an even number of values.
Mode is determined by identifying the data point that occurs most often. A
set of data may have more than one mode.
The mean is 69.8 inches. The median is 69.5 inches. The mode is 72 inches.
Since the data set is symmetric, the mean of 69.8 inches is best.
6.
Validate
If the data is a random sample from a larger population, collect a second
sample and see if the measures of central tendency are similar. If possible,
research the question to see what others have found. Compare with and
without outliers.
According to the CDC, the average height for men in the USA is 69.3 inches.
(Reference is online.)
7.1 Central Tendency