AQA A Level Maths: Statistics复习笔记2.1.3 Standard Deviation & Variance

The variance is another measure for the spread of the data, it measures the variability from the mean of the data.

What is the variance and the standard deviation?

• The variance is a statistic that tells us how varied a set of data is
  • Data that is more spread out will have a greater variance
  • Data that is consistent and close together will have a smaller variance
• The standard deviation is the square root of the variance
• The symbol for the population standard deviation is the lowercase Greek letter sigma, σ  and for variance is sigma squared, σ2
• Standard deviation and variance are used interchangeably within this course so make sure you look out for which one a question shows or asks for

How are the variance and standard deviation calculated?

• There is more than one formula that can be used for calculating the variance, and you should choose the most useful one
• Makes sure you know how to find these formulae in the formula booklet and are familiar with the version given

• The units for standard deviation are the same as the units for the data and the units for variance are the same as the units for the data but squared

How are the variance and standard deviation calculated from a frequency table?

• The method for finding the variance from a frequency table is similar to that of the mean