Shape of displays

1
Shape of displays
If a set of data is displayed as a frequency
polygon or histogram or a dot plot (or other
method of display), we can describe the features
of the curve such as its smoothness, symmetry and
mode. Remember if a curve has one mode it can
be called unimodal, if it has two modes it is
called bimodal. For a bimodal curve the two
distinct modes need not have the same frequency,
but look like two hills with a valley in
between. A curve is said to be symmetrical if it
is symmetrical about the mean. That is both
halves look the same and the peak is in the
middle. The mean, median and mode are all the
same value (the normal distribution or bell curve)
2
Skewed displays
A curve is said to be skewed (asymmetrical) if it
is a smooth curve with its mean and median to the
left or right of the mode.
Median
This curve is positively or right skewed. The
mean is to the right of the mode and median.
Mean - mode positive number
Mode
Mean
Median
This curve is negatively or left skewed. The mean
is to the left of the mode and median. Mean -
mode negative number
Mode
Mean
3
Skewed displays
Fishers rule, states that if there is more area
to the right of the mode, the curve is positively
or right skewed. If there is more area to the
left of the mode, the curve is negatively or left
skewed. If the data is skewed the median is
often the most appropriate measure of central
tendency. Clustering occurs when scores are
close together or bunched up.
4
Todays work
Exercise 8C page 245 1 - 4