Estimates in Statistics

In statistics, an estimate is a value or range of values used to infer information about a population based on data from a sample.
Since it’s often impractical to measure an entire population, we use estimates to make educated guesses about unknown population parameters (like the true mean or proportion).

In simple terms:

“We use a sample to estimate what’s true for the whole population.”

Two Main Types of Estimates

• Point Estimate - A single value used to estimate a population parameter. eg. Sample mean (𝑥̄) as an estimate of population mean (μ)
• Interval Estimate - A range of values that likely contains the true parameter, usually expressed as a confidence interval (CI). eg. 95% CI: 𝑥̄ ± margin of error

Point Estimate

A point estimate gives one “best guess” for a population parameter, based on sample data.

Examples:

• Sample mean (𝑥̄) estimates population mean (μ)
• Sample proportion (p̂) estimates population proportion (p)
• Sample variance (s²) estimates population variance (σ²)

Simple but uncertain: a single value can’t show how confident we are that it’s close to the true population value.

Interval Estimate (Confidence Interval)

An interval estimate gives a range of plausible values for a population parameter — not just a single number.
The most common form is the confidence interval (CI).

Formula (for the mean):

Where:

• 𝑥̄ = sample mean
• Z = Z-score from the standard normal distribution (e.g. 1.96 for 95% CI)
• σ = population standard deviation (or sample estimate)
• n = sample size

Interpretation

• A 95% confidence interval means that if we repeated sampling many times, about 95% of those intervals would contain the true population mean.
• It doesn’t mean there’s a 95% chance the mean is in this one interval — the parameter is fixed; the interval varies.

Confidence intervals show both estimate and uncertainty.

Common Confidence Levels

Example

If your sample mean = 50, standard deviation = 10, and sample size = 100:

95% Confidence Interval = (48.04, 51.96)
You’re 95% confident that the true population mean lies between 48.04 and 51.96.

In Machine Learning

• Model evaluation - Confidence intervals around performance metrics (accuracy, precision, recall)
• Feature analysis - Estimating uncertainty in feature effects or coefficients
• A/B testing - Determining if performance differences are statistically significant
• Sampling models - Estimating population parameters from subsets of data