# Point Estimate in Statistics: Definition, Formula & Example

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• 0:00 What Is a Point Estimate?
• 0:55 Estimating Parameters
• 1:38 Estimating With Accuracy
• 1:40 Calculating Point Estimates
• 3:00 Estimating With Confidence
• 3:35 Lesson Summary

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Lesson Transcript
Instructor: Tracy Payne, Ph.D.

Tracy earned her doctorate from Vanderbilt University and has taught mathematics from preschool through graduate level statistics.

In this lesson, you will be introduced to the point estimates used to estimate population parameters, the formula to calculate each, and how to reduce error and increase accuracy.

## What Is a Point Estimate?

Imagine you are trapped inside a dangerous dome with 20 game contestants who can only win the game by being the last person left alive. A little bird, a Mocking Jay perhaps, tells you that you can end the game by shooting an arrow into the sky and hitting some unknown point that will disable the power source of the city that put you there in the first place.

This is similar to what researchers and statisticians do: out of an arena of possible values, they try to pinpoint a single value that represents a population. The true value for the population is unknown. The only way the true value can be known is by a census, meaning we measure, count, or test every member in the population - in which case there is no need to estimate.

The point estimate is the statistic calculated from sample data used to estimate the true unknown value in the population called the parameter.

## Estimating Parameters

To estimate the true value for a population, we take samples from the population and use the statistics obtained from the samples to estimate the parameter. Here are a few examples of point estimates and when you might use each one:

• Sample means are used to find the center of continuous data.
• Sample proportions are used to find the mean part or share per whole.
• Sample standard errors describe the spread of data for means and proportions.

The following table displays some population characteristics researchers might try to estimate, each point estimate used to answer that question, the name of its symbol, the corresponding parameter and the name of its symbol:

Characteristic Point Estimate Symbol Parameter Symbol
Mean IQ of 3rd graders sample mean x-bar population mean mu
Proportion of college students who ride their bicycle to school sample proportion p-hat population proportion p
What is the variation in weight among Olympic female gymnasts sample standard error s population standard deviation sd or little sigma

## Calculating Point Estimates

The table below displays each point estimate and the formula used to calculate that statistic:

Point Estimate Symbol Description of Formula
sample mean x-bar sum all observations divided by the n (number of observations)
sample proportion p-hat the count of successful trials x divided by n (number of observations)
sample standard error for means s of x population standard deviation divided by the square root of n (number of observations)
sample standard error for proportions s of p (population proportion)*(1 - population proportion) divided by n (number of observations)

## Estimating With Accuracy

Just as wind and direction are important factors to your arrow's accuracy, so are bias and variability important factors to the accuracy of a researcher's point estimate.

High bias throws off the estimate causing the researcher to over or underestimate the center of the data. For example, if a researcher estimating the mean IQ of third graders selects a sample of third graders from the School of Gifted and Talented Students, his point estimate is likely to overestimate the mean for all third graders. To reduce bias, the researcher should have used a randomized sampling method.

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