## Mean, Variance, & Standard Deviation:

The three main measures in quantitative statistics are the mean, variance and standard deviation. These measures form the basis of any statistical analysis.

- Mean:
- Technically, the mean (denoted
*μ*), can be viewed as the most common value (the*outcome*) you would expect from a measurement (the*event*) performed repeatedly. It has the same units as each individual measurement value. - Variance:
- The variance (denoted
*σ*^{2}) represents the spread (the*dispersion*) of the repeated measurements either side of the mean. As the notation implies, the units of the variance are the square of the units of the mean value. The greater the variance, the greater the probability that any given measurement will have a value noticeably different from the mean. - Standard deviation:
- The standard deviation (denoted
*σ*) also provides a measure of the spread of repeated measurements either side of the mean. An advantage of the standard deviation over the variance is that its units are the same as those of the measurement. The standard deviation also allows you to determine how many significant figures are appropriate when reporting a mean value.

It is also important to differentiate between the population mean,
*μ*, and the sample mean, .