Here is the histogram of some times between eruptions of the
Old Faithful Geyser in minutes:
This histogram is not bell-shaped, so the center and spread are
not a good summary of the data.
Here are some histograms and the terms used to describe them:
The right-skewed and J-shaped histograms have
long right tails.
If a histogram is skewed, the median (Q2) is a better estimate of the
"center" of the histogram than the sample mean.
Other Measures of Central Tendency
A third another statistic that has been proposed
(in addition to the mean and median) to estimate the center of a
dataset: the 5%-trimmed mean: throw out the bottom 2.5% and top 2.5%
of the observations, then compute the sample mean of the remaining
The median and the 5%-trimmed mean are resistant
statistics because they are resistant to outliers.
If there are less than 2.5% outliers on the left and less than
2.5% outliers on the right, then the trimmed mean is more efficient for
estimating the center of the histogram than the median is.
A family of more esoteric statistics to estimate the center of
a dataset are the M-estimators. They are weighted averages, which
give heavier weight to the observations close to the median and less
weight to the observations in the tails.
To obtain M-estimators with SPSS, select
Analyze >> Descriptive Statistics >> Explore... Click the
Statistics button and check the M-estimators box.