# The Difference Between Statistics and Parameters

I. What is a parameter?

Definition: a numerical characteristic of a POPULATION (µ or σ)

Characteristics: A parameter is an unknown FIXED number. It is unknown because it describes a large population (where it is impossible to obtain data from the entire population). Therefore, although there exists an exact numerical value for the parameter, statisticians must estimate for it using a statistic.

II. What is a statistic?

Definition: a numerical characteristic of a particular SAMPLE (x̄ or p̂)

Characteristics: A statistic estimates for the parameter, is known because it is derived from the sample, and VARIES from sample to sample (due to sampling variability). A statistic describes a sample that was taken to estimate for the population; thus, a sample is an estimate for a particular parameter. It varies because the samples vary, thus it is unlikely to get the exact same statistic for more than one sample (although the statistics should be relatively close). Note: It is unnecessary to find a statistic if the parameter is known or if the population is small enough that the parameter can be found.

*Trick to Remembering: parameter describes a population and statistic describes sample (think p's and s's)*

Parameter Statistic
Mean µ x̅
Standard Deviation σ

III. Identifying a parameter or a statistic:

Example 1:

You want to determine the percent of people in your Statisitcs class that prefer chocolate to vanilla ice cream. You poll everyone in the class and find that 18 to 11 or 62% of your classmates prefer chocolate ice cream to vanilla ice cream. Is .62 a parameter or a statistic?

Answer: .62 is a parameter because in this study you collected data from your entire population; thus, it is not an estimation but the true value.

Example 2:

Now you want to determine the percent of people in your school that prefer chocolate to vanilla ice cream. You randomly poll 50 students when they walk into school in the morning. Your data shows that 34 to 16 or 68% of students prefer chocolate ice cream to vanilla ice cream. Is .68 a parameter or a statistic?

Answer: .68 is a statistic! You did not poll the entire school, but used the random sample of 50 students to estimate for the entire population of the school.