Differentiating between Estimator and Estimate:


An estimator is a statistical concept used in inferential statistics to make predictions or draw conclusions about a population based on sample data. It is a mathematical function or a rule that takes the observed sample data as input and produces an estimate, which is a numerical value that represents an approximation of an unknown population parameter.

Key Points:
- Estimators are used to estimate population parameters such as the mean, variance, proportion, regression coefficients, etc.
- They provide an approximation of the true value of the population parameter, which is often unknown and difficult to measure directly.
- Estimators are based on statistical principles and methods, which aim to minimize bias and maximize efficiency.
- Estimators can be classified into two types: point estimators and interval estimators.


A point estimator is a type of estimator that provides a single numerical value as an estimate of the population parameter. It uses the sample data to calculate a single value that is considered as the best guess for the population parameter.

Key Points:
- Point estimators are used when there is a need for a single numerical value to estimate the population parameter.
- Common point estimators include the sample mean, sample variance, sample proportion, etc.
- The sample mean, denoted as x̄, is a commonly used point estimator for the population mean, μ.
- Point estimators can be biased or unbiased. A biased estimator systematically overestimates or underestimates the population parameter, while an unbiased estimator has an expected value equal to the true population parameter.


An interval estimator is a type of estimator that provides a range of values as an estimate of the population parameter. It uses the sample data to calculate an interval within which the true value of the population parameter is likely to lie.

Key Points:
- Interval estimators are used when there is a need to estimate the population parameter with a certain level of confidence or probability.
- Common interval estimators include confidence intervals and prediction intervals.
- Confidence intervals provide a range of values within which the population parameter is likely to lie with a certain level of confidence.
- Prediction intervals provide a range of values within which an individual observation from the population is likely to fall with a certain level of confidence.


An estimate is the numerical value produced by an estimator. It is the result of applying an estimator to the observed sample data. An estimate is the best approximation of the unknown population parameter based on the available sample information.

Key Points:
- An estimate represents a single value or a range of values that is considered as the best guess for the population parameter.
- Estimates can be point estimates or interval estimates, depending on the type of estimator used.
- The accuracy and reliability of an estimate depend on various factors, such as the sample size, sampling method, variability of the data, and the quality of the estimator used.
- Estimates are used in hypothesis testing, decision making, and policy development, as they provide insights into the characteristics of the population based on the available sample information.

In conclusion, an estimator is a statistical concept or a mathematical function used to estimate population parameters, while an estimate is the numerical value produced by the estimator. The estimator provides an approximation of the true population parameter,