Reading and comparing data, choosing the best summary statistic, and spotting bias.
Practise Interpret, analyse and report data in the app →
What gets asked
- Read a value, or work out a fraction, from a graph, table or chart.
- Compare two data sets on the same issue.
- Choose the best summary statistic, mean, median or mode, for a data set.
- Identify a source of bias or error in how data was collected.
You must be able to
- Read values off a graph carefully, checking what each gridline represents.
- Check that two graphs use the same scale before comparing them.
- Choose the median over the mean when a data set has an outlier.
- Spot a leading question or an unrepresentative sample as a source of bias.
Traps that cost marks
- Comparing bars on two graphs without checking that their scales match. Always check the scale of both graphs before comparing their heights.
- Using the mean for a data set that has a large outlier. An outlier pulls the mean away from the typical value. The median is often fairer.
- Treating any surprising result as an error instead of checking the collection method. Look at how the data was collected before deciding a surprising result is wrong.
Worked example
- The mean is pulled up a lot by the R90 outlier.
- The median, the middle value once ordered, is barely affected by it.
- The median gives a fairer picture of what a typical friend spends.
Read and compare data
Reading a graph accurately, comparing two of them fairly, and saying what a prediction rests on.
- scale
- What one step on the axis is worth. It is not always one unit.
- trend
- The general direction the data moves in over time, ignoring small ups and downs.
- prediction
- A statement about data you do not have, based on the pattern in data you do.
Read the scale before you read a single bar. If the gridlines go up in fives, a bar three lines high is , not . Most misread graphs are misread here.
A pie chart shows shares of a whole, not counts. To turn a slice into a number you need the total, and the graph may not give it to you.
Comparing two graphs means comparing their scales first. Two bars the same height mean different things if one axis counts in tens and the other in hundreds.
Ask who the data came from and when. Two sets collected from different groups, or in different years, may not be comparable at all, however neat the graphs look.
A prediction rests on the trend, not on the last point. Say what you assumed, and remember the further past the data you go, the weaker the prediction gets.
Examples
Worked answer
- One gridline is worth .
- The bar reaches the fourth line.
- So the value is .
- .
Answer: 20
Counting lines instead of reading the scale would give 4, five times too small.
Worked answer
- Class A total: .
- Class B total: .
- Marks altogether: .
- Learners altogether: .
- Average: .
Answer:
The plain average of and is , which ignores that Class A is three times as big.
Worked answer
- Look at the trend across all six months, not only the last one.
- The trend is upward, so predict a further rise.
- State the assumption: that nothing changes about price, supply or customers.
- Say the prediction is for next month only, not for next year.
Answer: a further rise, if conditions stay the same
A trend can stop. A prediction with no assumption stated cannot be judged.
Traps
- Reading a bar as the number of gridlines when each line is worth more than one. Check the axis first. Four lines at each is .
- Comparing bar heights on two graphs without checking that the scales match. Read both axes first. Convert to the same scale before you say which is bigger.
- Choosing a pie chart for data that has to show change over time. A pie chart shows shares at one moment. Use a line graph for change over time.
- Predicting from the last data point on its own. Use the trend across all the data, and say how far ahead the prediction is meant to hold.
Bias, error and outliers
How the data was gathered, which single number to trust, and what one wild value does to an average.
- sample
- The smaller group actually asked or measured, standing in for everybody.
- bias
- A push in the data, from how it was gathered, that tilts the answer one way.
- error
- A wrong value, from a slip in measuring, recording or asking.
- outlier
- A value sitting far away from all the others in the set.
- extreme
- The smallest or the largest value in a set. It need not be an outlier.
- summary statistic
- One number that stands for a whole set, like the mean or the median.
Ask how the data was gathered before you believe it. A sample that did not stand for the whole group supports no conclusion or prediction about it.
Bias comes from the gathering, not from the numbers. A pushy question, or asking only at a taxi rank at dawn, tilts the answers before anyone counts them.
A surprising result is not automatically an error. Go back and look at how the data was collected. Sometimes the surprise is real and the method was sound.
The extremes are just the smallest and largest values. An outlier is more: it sits far from everything else. It drags the mean towards itself, because the mean uses every value.
The median only cares about position, so one wild value hardly moves it. With a big outlier the median is the fairer summary statistic. If you drop a value, say so and why.
Examples
Worked answer
- Add them: .
- Mean: .
- In order: ; ; ; ; .
- The middle one is , so that is the median.
- Four of the five spent under R23, so R31 fits nobody.
Answer: the median, R20
One value of R76 dragged the mean up. The median barely felt it.
Worked answer
- He asked only people who had already chosen his shop.
- That sample cannot stand for everyone in the street.
- The wording pushes them towards yes as well.
- Both who he asked and how he asked carry bias.
Answer: the sample and the wording are both biased
Bias can come from who you ask as much as from how you ask.
Worked answer
- Nobody carries a kg bag, so something is wrong.
- Check the record first: it may be kg, written down wrongly.
- If it truly is an error, correct it or leave it out.
- Either way, write down what you did and why.
Answer: no, check it first and then report what you did
Removing a value in silence changes the answer and hides the reason.
Traps
- Believing a conclusion drawn from a sample that did not stand for the whole group. Check who was actually asked before you accept what the data seems to say.
- Treating any surprising result as an error instead of checking the collection method. Look at how the data was collected before deciding a surprising result is wrong.
- Using the mean for a data set that has a large outlier. An outlier pulls the mean away from the typical value. The median is often fairer.
- Dropping an outlier quietly, without telling the reader. Say which value you left out and why, so the reader can check your work.