Parameter & Statistics | Applied Mathematics for Class 12 - Commerce PDF Download

Population vs Sample

You want to identify the level of support for the death penalty among US residents. Since the population you’re interested in is all US residents, it’s not practical to collect data from the whole population. Instead, you use random sampling to survey a sample of 2000 participants.

What kinds of numbers are parameters and statistics?

• Statistics and parameters are numbers that summarize any measurable characteristic of a sample or a population.
• For categorical variables (e.g., political affiliation), the most common statistic or parameter is a proportion.
• For numerical variables (e.g., height), the mean or standard deviation are commonly reported statistics or parameters.

Examples of Statistics vs Parameters

Statistical Notation

• Different symbols are used for statistics versus parameters to show whether a sample or a population is being referred to.
• Greek letters and capital letters usually refer to populations, whereas Latin letters and lower-case letters refer to samples.

Symbols for statistics vs parameters

Estimating Parameters from Statistics

Using inferential statistics, you can estimate population parameters from sample statistics. To make unbiased estimates, your sample should ideally be representative of your population and/or randomly selected.
There are two important types of estimates you can make about the population parameter: point estimates and interval estimates.

• A point estimate is a single value estimate of a parameter based on a statistic. For instance, a sample mean is a point estimate of a population mean.
• An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.

Both types of estimates are important for gathering a clear idea of where a parameter is likely to lie.

Estimating a population parameter from a sample statistic
In your study on support for the death penalty among US residents, you find that 61% of participants in your sample support the death penalty. To estimate the population parameter, you calculate a point estimate and an interval estimate from your sample statistic.
Your point estimate is your sample statistic – you estimate that 61% of all US residents support the death penalty.
To find the interval estimate, you construct a 95% confidence interval that tells you where the population parameter is expected to lie most of the time. With random sampling, there is a 0.95 probability that the true population parameter for support for the death penalty among US residents lies between 57% and 65%.