Statistical Definitions and Formulas

Population is the entire group of individuals or objects that are considered.

Sample is a subset of the population whose characteristics are being analyzed with the intent of making a statement about the entire population.

Sample size, n=number of objects or individuals in the sample.

Statistic is a number associated with a sample for the purpose of describing some property of the sample.

Statistics

When a numerical measurement x is associated with each element of the sample, certain descriptive statistics can be calculated

Sample mean, =is a measure of the central tendency of the numbers

Sample variance, is a measure of how widely dispersed are the numbers .

Sample standard deviation is a measure of the average difference between the sample mean and each of the numbers . The smaller this is the more closely clustered are the numbers.

Standard error of the mean, is a measure of dispersion we could get if we took many different samples from one population, calculated the mean of each sample, and then used the sample means as our data points.

Formulas

Volumes:

· Volume of a block=

· Volume of a cylinder=

The radius is half the diameter

· Volume of a sphere =

The radius is half the diameter

· Density = mass/Volume

In these latter formulas, use the appropriate number of significant digits of

Statistics:

Given a set of numbers

sample size = n,

mean, =

variance,

standard deviation

standard error of the mean, .

Given two data sets A and B with means and , sample sizes and , and standard deviations and , the

t-statistic is