**Measures of Central Tendency**

**Mean**

Here

**Geometric Mean**

- taking the logarithm of each number
- computing the arithmetic mean of the logarithms
- raising the base used to take the logarithms to the arithmetic mean.

**Harmonic Mean**

The harmonic mean is used to take the mean of sample
sizes. If there are

**Median**

When there is an odd number of numbers, the median is
simply the middle number. For example, the median of 2, 4,
and 7 is 4.
When there is an even number of numbers, the median is the
mean of the two middle numbers. Thus, the median of the
numbers 2, 4, 7, 12 is

**Mode**

The mode is the most frequently occurring score in a distribution and is used as a measure of central tendency.

**Trimean**

The trimean is computed by adding the 25th percentile plus twice the 50th percentile plus the 75th percentile and dividing by four.

**Trimmed Mean**

A trimmed mean is calculated by discarding a certain percentage of the lowest and the highest scores and then computing the mean of the remaining scores. For example, a mean trimmed 50% is computed by discarding the lower and higher 25% of the scores and taking the mean of the remaining scores. The median is the mean trimmed 100% and the arithmetic mean is the mean trimmed 0%.

**Measures of Spread**

**Range**

The range is the simplest measure of spread or dispersion: It is equal to the difference between the largest and the smallest values.

**Semi-interquartile Range**

The semi-interquartile range is a measure of spread or
dispersion. It is computed as one half the difference
between the 75th percentile [often called
(

**Variance and Standard Deviation**

The variance in a population is:

The standard deviation is the square root of the variance. It is the most commonly used measure of spread.

**Shape**

**Skew**

Skew can be calculated as:

**Kurtosis**

Kurtosis is based on the size of a distribution's tails. Distributions with relatively large tails are called "leptokurtic"; those with small tails are called "platykurtic." A distribution with the same kurtosis as the normal distribution is called "mesokurtic." The following formula can be used to calculate kurtosis: