When one is examining a
histogram there are generally two elements that are examined. The first are the three averages of the
set presented: the
mean,
mode, and
median. The other is the spread of the set. For example, the set:
{1,2,5,5,5,8,9}
Has a
mean of five, a
mode of five, and a
median of five. This is also true of the set:
{0,1,4,5,6,9,10}
Except that there is no
mode since each value has equal
frequency. Regardless of the fact that these two
sets have different
central tendencies they are nevertheless not
identical. The difference is in the spread of the two
sets. Spread is a reflection of how the various values are placed
relative to the
mean value of the
set. The most common way to measure spread is with
standard deviation.
Standard deviation is equal to the
square root of the
mean of the
deviations of the
set squared, as explained in the
node standard deviation.