Fall 26
A parameter is a numerical summary of a population.
A statistic is a numerical summary of a sample.
| Summary | Population parameter | Sample statistic |
|---|---|---|
| Mean | \mu | \bar{x} |
| Proportion | p | \hat{p} |
Hopefully, \bar{x} is close to \mu.
Hopefully, \hat{p} is close to p.
A retailer wants to know the mean amount spent on all its online orders last month. A sample of 450 orders has a mean of $85.37.
A retailer wants to know the mean amount spent on all its online orders last month. A sample of 450 orders has a mean of $85.37.
| Summary | Description or value |
|---|---|
| Population parameter | ? |
| Sample statistic | ? |
What is the parameter? Do we know its value?
What is the statistic? What is its value?
A retailer wants to know the mean amount spent on all its online orders last month. A sample of 450 orders has a mean of $85.37.
| Summary | Value |
|---|---|
| Mean for all online orders last month (\mu) | Unknown |
| Sample mean (\bar{x}) | $85.37 |
The $85.37 is a statistic because it describes the 450 sampled orders.
A researcher wants to know the proportion of all FIT students who are left-handed this semester. In a sample of 200 students, 26 are left-handed.
A researcher wants to know the proportion of all FIT students who are left-handed this semester. In a sample of 200 students, 26 are left-handed.
| Summary | Description or value |
|---|---|
| Population parameter | ? |
| Sample statistic | ? |
What is the parameter? Do we know its value?
What is the statistic? What is its value?
A researcher wants to know the proportion of all FIT students who are left-handed this semester. In a sample of 200 students, 26 are left-handed.
| Summary | Value |
|---|---|
| Proportion of all FIT students who are left-handed (p) | Unknown |
| Sample proportion (\hat{p}) | 26/200 = 0.13\ (13\%) |
The 13% is a statistic because it describes the 200 sampled students.
A factory made 1,000 jackets yesterday. Records for all 1,000 show a mean sewing time of 42 minutes. A sample of 50 of these jackets has a mean of 44 minutes.
A factory made 1,000 jackets yesterday. Records for all 1,000 show a mean sewing time of 42 minutes. A sample of 50 of these jackets has a mean of 44 minutes.
| Summary | Description or value |
|---|---|
| Population parameter | ? |
| Sample statistic | ? |
What is the parameter? Do we know its value?
What is the statistic? What is its value?
A factory made 1,000 jackets yesterday. Records for all 1,000 show a mean sewing time of 42 minutes. A sample of 50 of these jackets has a mean of 44 minutes.
| Summary | Value |
|---|---|
| Mean for all 1,000 jackets (\mu) | 42 minutes |
| Mean for the 50 sampled jackets (\bar{x}) | 44 minutes |
The 42 minutes is a parameter. The 44 minutes is a statistic.
A production run contains 2,000 zippers. An inspection of every zipper finds 60 defective ones. A sample of 100 zippers from the run contains 4 defective ones.
A production run contains 2,000 zippers. An inspection of every zipper finds 60 defective ones. A sample of 100 zippers from the run contains 4 defective ones.
| Summary | Description or value |
|---|---|
| Population parameter | ? |
| Sample statistic | ? |
What is the parameter? Do we know its value?
What is the statistic? What is its value?
A production run contains 2,000 zippers. An inspection of every zipper finds 60 defective ones. A sample of 100 zippers from the run contains 4 defective ones.
| Summary | Value |
|---|---|
| Defective proportion in the entire run (p) | 60/2000 = 0.03\ (3\%) |
| Defective proportion in the sample (\hat{p}) | 4/100 = 0.04\ (4\%) |
The 3\% is a parameter. The 4\% is a statistic.
A researcher wants to know the mean weekly study time of all FIT students this semester. One sample of 200 students has a mean of 13.5 hours. Another sample of 200 has a mean of 14.2 hours.
A researcher wants to know the mean weekly study time of all FIT students this semester. One sample of 200 students has a mean of 13.5 hours. Another sample of 200 has a mean of 14.2 hours.
| Summary | Description or value |
|---|---|
| Population parameter | ? |
| Sample statistic | ? |
What is the parameter? Do we know its value?
What is the statistic? What is its value?
A researcher wants to know the mean weekly study time of all FIT students this semester. One sample of 200 students has a mean of 13.5 hours. Another sample of 200 has a mean of 14.2 hours.
| Summary | Value |
|---|---|
| Mean for all FIT students (\mu) | Unknown |
| Two sample means (\bar{x}) | 13.5 and 14.2 hours |
Both sample means are statistics. Different samples can give different values.
A parameter describes the entire population of interest.
A statistic describes a sample from that population.
For a fixed population, a parameter has a fixed value, even when we do not know it. A statistic can vary from sample to sample.
We use a sample statistic to estimate an unknown population parameter.