## CHAPTER SUMMARY

### I. Standard Deviation

Standard Deviation

#### Mean

The arithmetic mean is a number often used to describe the “average” value of a data set. The arithmetic mean is defined as:

mean = \dfrac{sum \,of\, the \,values}{number \,of \,values}

#### Median

The median is the “middle” value. To find the median, arrange the values in numerical order. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the mean of the two middle values.

#### Range

The range is a number that describes the spread or dispersion of a data set. The range is the difference between the largest and smallest values.

range = (greatest value) – (least value)

#### Standard Deviation

The standard deviation compares data by looking at how much the numbers in a set differ, or deviate, from the mean. The greater the difference, the greater the standard deviation.

The formula for standard deviation is

sd = \sqrt{\dfrac{sum \,of\, (each \,value \,-\, mean)^{\displaystyle{2}}}{number \,of \,values}}

### II. Normal Distribution

Normal Distribution

The normal distribution is a way to model data using the standard deviation.  It is used to describe data that clusters around the arithmetic mean.

The normal curve is a graphical model of a normal distribution.  The graph won’t be shown on the GMAT, but visualizing it lets you quickly calculate the percent of data above or below a given value using the standard deviation. 