# Sampling and Normal Distribution

## What do you need to be able to do?

1. Sampling
2. Comparing populations and samples
3. The capture-recapture technique
4. The normal distribution
5. z-scores

## 1. Sampling

Key terms

• Population: total number of items being studied
• Census: survey of ALL the population
• Sample: a smaller group of the population

Main types of samples:

• Random sample: each item equally likely to be chosen from the population,
• Systematic sample: items chosen on regular intervals, e.g. every tenth car
• Stratified sample: a random sample is taken from each stratum/layer of a population. E.g. if a population contains 70% adults and 30% children then sample will contain 70% adults and 30% children

## 2. Comparing samples and population

You need to know:

## 3. Capture-Recapture Technique

Capture-recapture technique is a way of estimating the size of a population.

Estimated Population = (number tagged x number captured) / (number tagged and recaptured)

What a video here

## 4. Normal Distribution

Normal distribution is a bell-shaped curve.

• 68% of scores lie within one standard deviation from the mean
• 95% of scores lie within two standard deviations of the mean
• 99.7% of scores lie within three standard deviations of the mean

## 5. Z-Scores

A z-score (standardised score) shows the position of a 'raw' score relative to the mean.

The distribution of z-scores is a normal distribution with a mean of 0 and a standard deviation of 1