Explain briefly Point and Interval estimations.
Answers
Estimating in Statistics
Anna is an animal lover and volunteers at a local animal shelter in her town. She wants to make a proposition to the city council to create a dog park in the town. She wants to gather some data about the opinions of the town. Because she can't survey the entire town, she will need to collect data from a few people and make an estimation. An estimation is the tool that is used in mathematics to make inferences about populations from data.
In this lesson, you will learn about two types of estimation: point and interval estimation. Let's begin with point estimation as we follow Anna's story.
Point Estimation
Anna surveys 100 random people out of her town about building a dog park. This is known as a sample. A sample is a part of a population used to describe the whole group. Anna will use the data that she gathers from this sample to describe the population of the town. The data Anna gathers will be statistics.
A statistic is the characteristics of a sample used to infer information about the population. For example, Anna may include questions on her survey such as age and number of pets. If the mean age for her sample is 32, then 32 is a sample statistic. She might infer that the average age of the people in town is also 32.
A point estimation is a type of estimation that uses a single value, a sample statistic, to infer information about the population. Point estimation can be a sample statistic. The sample mean of age for the sample, 32, can be used as a point estimation.
Point estimation is a single value that can be inferred as a population parameter. Let's discuss populations, parameters, and their relationship to point and interval estimations.
Interval Estimation
After Anna collected her data from the survey, she can now draw inferences from her sample statistics about the population. A population is all members of a specified group. In this case, the population is literally the population of a town. However, a population can mean many things. For example, if you are doing research about college students, then your population would be all college students. If your research is about high school athletes, then your population would be all high school athletes. It's mostly up to the researcher to define the population.
Once sample information is gathered, the researcher can make inferences about the population, known as a parameter. A parameter is the characteristics used to describe a population. You can use a sample statistic to develop population parameters. For example, Anna found that of the 100 people she surveyed, each household owns an average of two pets. This is a sample statistic. However, Anna can also use this statistic to infer that everyone in the population also owns an average of two pets; at this point it is considered a population parameter. If we were estimating from a single value, such as the average of two pets, then we could say that this population parameter was a point estimation.
However, what about the people that own more than two pets or no pets? Can 100 people really show us the characteristics of an entire town? This is where interval estimation comes in handy. Interval estimation is the range of numbers in which a population parameter lies considering margin of error. Because there is a certain level of uncertainty, an interval estimate gives a range, rather than a single value, of the population parameters.