### Introduction to Estimation of Population Parameters

In statistics, estimating population parameters is important because it allows the researcher to conclude a population (whole group) by analyzing a small part of that population. The estimation of population parameters is done when the population under study is large enough. For example, instead of performing a census, a random sample from the population can be drawn. To draw some conclusions about the population, one can calculate the required sample statistic(s).

## Table of Contents

### Important Terminologies

The following are some important terminologies to understand the concept of estimating the population parameters.

**Population:**The entire collection of individuals or items one is interested in studying. For instance, all the people living in a particular country.**Sample:**A subgroup (or small portion) chosen from the population that represents the larger group.**Parameter:**A characteristic that describes the entire population, such as the population mean, median, or standard deviation.**Statistic:**A value calculated from the sample data used to estimate the population parameter. For example, the sample mean is an estimate of the population mean. It is the characteristics of the sample under study.

Various statistical methods are used to estimate population parameters with different levels of accuracy. The accuracy of the estimate depends on the size of the sample and how well the sample represents the population.

We use statistics calculated from the sample data as estimates for the population parameters.

**Sample mean:**is used to estimate the population mean. It is calculated by averaging the values of all observations in the sample, that is the sum of all data values divided by the total number of observations in the data.**Sample proportion**: is used to estimate the population proportion (percentage). It represents the number of successes (events of interest) divided by the total sample size.**Sample standard deviation:**is used to estimate the population standard deviation. It reflects how spread out the data points are in the sample.

### Types of Estimates

There are two types of estimates:

**Point Estimate:**A single value used to estimate the population parameter. The example of point estimates are:- The mean/average height of Boys in Colleges is 65 inches.
- 65% of Lahore residents support a ban on cell phone use while driving.

**Interval Estimate:**It is a set of values (interval) that is supposed to contain the population parameter. Examples of interval estimates are:- The mean height of Boys in Colleges lies between 63.5 and 66.5 inches.
- 65% ($\pm 3$% of Lahore residents support a ban on cell phone use during driving.

### Some Examples

Estimation of population parameters is widely used in various fields of life. For example,

- a company might estimate customer satisfaction through a sample survey,
- a biologist might estimate the average wingspan of a specific bird species by capturing and measuring a small group.