Measuring the center
The Mode
The Mean
The Median M is the midpoint of a distribution, the number such that half
the observations are smaller and the other half are larger. To find the
median of a distribution:
1. Arrange all observations in order of size, from smallest to largest.
2. If the number of observations n is odd, the median M is the center
observation in the ordered list. If the number of observations n is
even, the median M is midway between the two center observations
in the ordered list.
3. You can always locate the median in the ordered list of
observations by counting up (n + 1)/2 observations from the start of
the list.
COMPARING THE MEAN AND THE MEDIAN
The mean and median of a roughly symmetric distribution are close
together. If the distribution is exactly symmetric, the mean and median are
exactly the same. In a skewed distribution, the mean is usually farther out in
the long tail than is the median.
Measuring spread
The Range
The Variance
The Standard derivation
The Quartiles
To calculate the quartiles:
1. Arrange the observations in increasing order and locate the median
M in the ordered list of observations.
2. The first quartile Q1 is the median of the observations whose
position in the ordered list is to the left of the location of the overall
median.
3. The third quartile Q3 is the median of the observations whose
position in the ordered list is to the right of the location of the overall
median.
Measuring the shape
The Skewness
The Kurtosis
THE FIVE-NUMBER SUMMARY
The five-number summary of a distribution consists of the smallest
observation, the first quartile, the median, the third quartile, and the largest
observation, written in order from smallest to largest. In symbols, the five-
number summary is Minimum Q1 M Q3 Maximum. They are represented in
the boxplot:
