Symbols and Their Meaning

Below are the some of the symbols that represent parameters and statistics that are used in elementary statistics.

  • x     The random variable that represents the quantitative outcome.  For example, if a survey is conducted asking 100 people how much they weigh, then x is a randomly selected respondents weight
  • m     The population mean.  For example, for the survey that asks 100 people's weight, m represents the average weight of all people in the world, not just from the survey respondents.

  • xBar     The sample mean.  For example, for the survey that asks 100 people's weight, xBar represents the average weight of the 100 respondents.

  • mu sub xBar     The population mean of the sampling distribution.  For example, consider every possible group of 100 people.  Each one of these groups will have its own sample mean xBar, the mean of all of these many many xBar's will be the population mean of the sampling distribution mu sub xBar.

  • s     The population standard deviation.  For example, for the survey that asks 100 people's weight, s represents the standard deviation of all people in the world, not just from the survey respondents.

  • s     The sample standard deviation.  For example, for the survey that asks 100 people's weight, s represents the standard deviation of the 100 respondents.

  • sigma sub xBar     The population standard deviation of the sampling distribution.  For example, consider every possible group of 100 people.  Each one of these groups will have its own sample standard deviation xBar, the standard deviation of all of these many many xBar's will be the population standard deviation of the sampling distribution sigma sub xBar.

  • p     The population proportion.  For example, if a survey is conducted of 100 randomly selected Americans asking them if they were born in America, then p is the proportion of all Americans who were born in America not just the 100 Americans who were surveyed.

  • pHat     The sample proportion.  For example, if a survey is conducted of 100 randomly selected Americans asking them if they were born in America, then pHat is the proportion of the 100 Americans who were surveyed that were born in American.

  • mu sub pHat     The population mean of the sampling distribution for proportions.  For example, consider every possible group of 100 people.  Each one of these groups will have its own sample proportion pHat, the mean of all of these many many pHat's will be the population mean of the sampling distribution for proportions mu sub pHat.

  • sigma sub pHat     The population standard deviation of the sampling distribution for proportions.  For example, consider every possible group of 100 people.  Each one of these groups will have its own sample proportion pHat, the standard deviation of all of these many many pHat's will be the population standard deviation of the sampling distribution for proportions sigma sub pHat.