Key learning outcomes for this video:

• To be able to create a stratified sample.
• To be able to plot a scatter graph and draw and interpret a line of best fit.
• To recognise and interpret different types of correlation on a scattergraph.

Cue card notes and useful reminders

• Stratified sampling is used to select a sample that is representative of different groups. If the groups in the original data are of different sizes, the number of items selected from each group will be proportional to the number of items in that group.
• A scattergraph can be used to represent data where we are looking for a relationship between the two variables.
• A variable is any characteristic, number, or quantity that can be measured or counted. They can be qualitative (a category) or quantitative (numeric). Quantitative variables can be discrete (take specific values, e.g. shoe size) or continuous (take any value depending how accurately you are measuring, e.g. foot length).
• Different types of correlation:

• A line of best fit roughly follows the pattern of the data points. It does NOT have to go through any points or start on the axes. You can use a line of best fit to make further predictions.
• The closer the data is grouped around the line of best fit the STRONGER the correlation. The more spread out the data is from the line of best fit the WEAKER the correlation. 

The video discusses creating a stratified sample to represent a larger group of data, using fractions to calculate how many students to select from each course. The video then shows how to plot a scatter graph and draw a line of best fit to recognize and label a correlation between two variables, using the example of test scores and hours revised.

The video explains that a positive correlation suggests an increase in test scores as hours revised increases and how to predict test scores based on hours revised. The video also covers the topic of outliers and the limitations of predicting outcomes beyond the bounds of a dataset. The video ends by discussing how to describe the strength of a correlation using scatter graphs and lines of best fit.

Key learning outcomes for this video:

1. To be able to create a stratified sample.

2. To be able to plot a scatter graph and draw and interpret a line of best fit.

3. To recognise and interpret different types of correlation on a scattergraph.

Sampling refers to the process of selecting a representative subset of data from a larger population. A stratified sample involves dividing the population into subgroups, or strata, based on a specific characteristic or variable, and then selecting a random sample from each stratum. This ensures that the sample is representative of the entire population and can help to reduce bias in the data.

A scatter graph is a type of graph used to display data that involves two numerical variables. Each data point is plotted as a point on the graph, with one variable plotted on the x-axis and the other variable plotted on the y-axis. A line of best fit can be drawn through the data points to show the general trend of the data. The line of best fit can be used to make predictions or estimate values for one variable based on the value of the other variable.

When interpreting a scatter graph, it's important to look for patterns and relationships between the two variables. Different types of correlation can be observed on a scatter graph, such as positive correlation (when an increase in one variable is associated with an increase in the other variable), negative correlation (when an increase in one variable is associated with a decrease in the other variable), or no correlation (when there is no clear relationship between the two variables).

In the GCSE Maths exam, students may be asked to demonstrate their understanding of sampling and scatter graphs in a few different ways.

With regards to sampling, students may be asked to:

1. Identify the advantages and disadvantages of different sampling methods (such as random sampling, stratified sampling, or quota sampling).

2. Design and carry out a survey or experiment using a particular sampling method.

3. Analyze and interpret data from a sample, and draw conclusions about the larger population based on the sample data.

With regards to scatter graphs, students may be asked to:

1. Plot data points on a scatter graph, and draw a line of best fit through the data.

2. Calculate and interpret correlation coefficients to determine the strength and direction of the relationship between the two variables.

3. Use the line of best fit to make predictions or estimate values for one variable based on the value of the other variable.

4. Interpret real-world scenarios represented by scatter graphs, and draw conclusions or make predictions based on the data.

It's important for students to understand not just how to perform these operations, but also the reasoning behind them. For example, students should understand why a stratified sample is often more representative than a simple random sample, or why a strong correlation on a scatter graph doesn't necessarily imply causation. By demonstrating a deep understanding of the concepts, students will be better equipped to succeed on the GCSE Maths exam and in their future studies.