Reading and completing line graphs

Line graphs are an effective tool for displaying data that changes over time. They consist of points connected by lines, making it easy to observe trends or patterns across a specific period.

Steps to read a line graph

• Locate the x-axis value - Identify the specific value on the horizontal axis that you need to investigate.
• Trace upwards - Follow a vertical line from this point up to the line on the graph that represents the data set you're interested in.
• Read across to the y-axis - From the point on the line, move horizontally to the vertical axis to determine the corresponding value.

Example: To find out how much coal was produced in northern England in 1919, locate 1919 on the x-axis, move up to the line representing northern England, then read across to the y-axis. If the value is 50, and the scale is in millions of tonnes, the production was 50 million tonnes.

Steps to complete a line graph

• Find the x-axis value - Identify the relevant point on the horizontal axis for the data you need to plot.
• Move up to the y-axis value - Go vertically upwards to the correct value on the vertical axis, ensuring you're aligned with the x-axis point.
• Mark the point and connect - Place a dot at this position and use a ruler to join it to the existing line.

Example: To plot that South Wales produced 20 million tonnes of coal in 1929, find 1929 on the x-axis, move up to 20 on the y-axis, mark the point, and connect it to the existing South Wales line with a ruler.

Describing trends in line graphs

When asked to describe what a graph shows, focus on key patterns and significant points in the data. This involves identifying changes over time and highlighting important highs and lows.

Key elements to describe in line graphs

• Upward trends - Note periods where the data increases.
• Downward trends - Identify sections where the data decreases.
• Peaks - Mention the highest point on the graph.
• Troughs - Point out the lowest value.

Example: The population fell between 1990 and 1991, then increased until 1993 when it began to fall again. The population was highest in 1993 at 100,000, and was lowest in 1991 at 20,000.

Understanding scatter graphs and correlation

Scatter graphs are used to show the relationship between two variables by plotting individual data points on a grid. They help in identifying whether and how two factors are connected through a concept called correlation.

Types of correlation in scatter graphs

• Positive correlation - When one variable increases as the other increases, the points on the graph trend upwards from left to right.
• Negative correlation - When one variable decreases as the other increases, the points trend downwards from left to right.
• No correlation - If the points are randomly scattered with no clear trend, there is no relationship between the variables.

Example 1 (Positive correlation): As height increases, rainfall also increases. The line slopes up from left to right, showing a positive correlation.

Example 2 (Negative correlation): As height increases, temperature decreases. The line is sloping down to the right, indicating a negative correlation.

Example 3 (No correlation): A scatter graph of altitude against soil acidity shows points spread randomly across the chart with no discernible pattern, indicating no correlation between the two variables.

Interpreting best fit lines in scatter graphs

A best fit line is a straight line drawn through the data points on a scatter graph to represent the overall trend. It helps in visualising the type of correlation between the variables.

Using best fit lines to analyse trends

• Drawing the line - Sketch a line that passes as close as possible to most of the points.
• Interpreting the slope - An upward sloping line indicates a positive correlation, while a downward sloping line shows a negative correlation. If no line can be reasonably drawn due to scattered points, there is no correlation.
• Application - The best fit line can be used to predict values not directly measured by estimating where a point would fall based on the trend.

Example: In a scatter graph showing the relationship between height above sea level and annual rainfall, a best fit line sloping upwards confirms a positive correlation, suggesting that higher altitudes generally experience more rainfall.