Toss a well-balanced coin once and the probability of heads is 0.5. and the
probability of tails is 0.5.
Tossed twice the probability of heads once is 0.5, heads twice is
0.250, and not at all is 0.250
Tossed three times the probability of heads once is 0.3750, twice is
0.3750, three times is 0.1250 and not at all is 0.1250.
Spread or Dispersion.
Spread, or dispersion, refers to how far out our figures go. A chunk of
butter on a slice of bread is hardly spread at all. The same chunk can be
spread out thickly or thinly. The larger area it covers, he more its
spread. It is the same with figures.
The first
array of figures is thinly spread:
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,
7, 7, 7, 7, 8, 8, 8, 9, 9
The second
array of figures is thickly spread:
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6
Nevertheless, the
averages of the figures are the same: The
arithmetical mean is
170, the
median and the
mode are both 5.
For the dataset {2, 3, 5, 8, 12} the mean is 6. So
the deviations from the mean are {-4, -3, -1, 2, 6}. We square these
deviations, {16, 9, 1, 4, 36}, and take their average, 13.2. Finally we
take the
square root of 13.2 to give us the Standard Deviation, 3.63.