Scatter Graphs & Correlation Flashcards

All 12 cards in this deck

What does a scatter graph show?

The relationship between two variables measured for each item (bivariate data), with one variable on each axis.

What are the steps to plot bivariate data on a scatter graph?

e.g. a student scored 34 in Science and 38 in Maths, with Science on the $x$-axis

1. Take the first variable as the $x$-value: $x = 34$
2. Take the second variable as the $y$-value: $y = 38$
3. Mark a cross at that point: a cross at $(34, 38)$

What type of correlation is shown when one variable decreases as the other increases?

Negative correlation.

e.g. as rainfall increases, hours of sunshine decrease.

On a scatter graph, what does it mean to say the correlation is strong?

The points lie close to a straight line.

Weak correlation means the points are more spread out from a line.

What is an outlier on a scatter graph, and how do you write down your answer when asked to identify one?

A point that does not fit the trend of the other points (far away from the others); write it as coordinates, e.g. $(10, 19)$.

True or false? A scatter graph showing positive correlation between ice cream sales and numbers of sunburn cases proves that eating ice cream causes sunburn.

False. Correlation does not indicate causation — another factor (hot, sunny weather) could be affecting both.

What is a line of best fit on a scatter graph?

A single straight line drawn through the middle of the points, following the trend, with roughly equal numbers of points on each side.

True or false? A line of best fit must pass through the origin.

False. It just has to follow the trend of the points — it should not be forced through the origin or through one particular point.

What are the steps to estimate a value from a scatter graph using a line of best fit?

e.g. estimate the Maths mark of a student with a Science mark of $34$ (Science on the $x$-axis)

1. Draw a suitable straight line of best fit.
2. Draw a line up from the known value on its axis to the line of best fit: up from $x = 34$.
3. Read across to the other axis: gives an estimated Maths mark of about $38$.

What is interpolation when using a line of best fit?

Estimating a value that lies inside the range of the plotted data, which makes the estimate reasonably reliable.

Why may an estimate found by extending a line of best fit beyond the plotted points be unreliable?

Because it is extrapolation — the value is outside the range of the data, so the trend may not continue.

What does the gradient of a line of best fit tell you in context?

e.g. ship width (m) against ship length (m), gradient $0.15$

The average change in the $y$-variable for each increase of $1$ in the $x$-variable: width increases by about $0.15$ m for each extra metre of length.