Reading, comparing and questioning data shown in graphs, then reporting on it.
Practise Interpret, analyse and report data in the app →
What gets asked
- Read a value off a bar graph, pie chart or histogram.
- Explain how the scale of a graph affects the impression it gives.
- Explain how an extreme value affects the mean, median or range.
- Write a short report with a conclusion drawn from a data set.
You must be able to
- Read the correct axis and the correct bar or sector.
- Notice when an axis does not start at zero.
- Explain why the median can suit data with an extreme value better than the mean.
- Support a conclusion or prediction with the data, not just a guess.
Traps that cost marks
- Assuming the vertical axis of every graph starts at zero. Check the starting value on the axis before comparing bar heights. It can make a small difference look huge.
- Assuming one very large or very small value cannot change the mean. The mean uses every value, so one extreme value can pull it a long way.
- Reading the value from the wrong bar or the wrong axis on a graph. Check the label and the axis carefully before reading off a value.
- Choosing the mean to represent a data set that has an extreme value. When there is an extreme value, the median usually represents the data better than the mean.
Worked example
- The R2 000 day is an extreme value that pulls the mean upward.
- The median is not affected by how far away one value is, only by its position.
- The median gives a fairer picture of a typical day.
Read graphs and spot trends
Reading a graph without being fooled by it, and saying where the data seems to be going.
- scale
- What one step on the side of a graph is worth. Not always one.
- gridline
- One of the lines across a graph. Each marks a step on the scale.
- key
- The note on a graph saying which colour or bar stands for which group.
- trend
- The direction the data moves in over time, ignoring small ups and downs.
- prediction
- A statement about data you do not have, from the pattern in data you do.
Read the scale before you read a single bar. Check what one gridline is worth. Where the gridlines go up in fives, a bar three lines high shows .
Then check the right bar. A double bar graph has two bars above each label, so read the key first. Taking the wrong bar is the commonest slip.
A pie chart gives shares, not counts. To turn a slice into a number you also need the total. Two pictures of one data set never disagree. Each hides what the other shows.
Where the side of a graph starts changes the impression. A graph beginning at instead of makes a small gap look enormous. Check that bottom number first.
A trend is the direction the data moves over the whole graph, not just at the end. Base a prediction on the trend. Say what you assumed, and how far ahead it holds.
Examples
Worked answer
- One gridline is worth .
- The bar reaches the third one.
- .
Answer: learners
Counting the gridlines instead of reading the scale would give .
Worked answer
- A quarter of the learners take taxis: .
- The bar graph shows learners too.
- So the two graphs say the same thing.
- The pie chart gave the share; the bar graph gave the count.
Answer: no, both say learners
One data set cannot argue with itself. Only the way of showing it changed.
Worked answer
- The real gap is learners.
- But the graph starts at , not at .
- So the first bar is steps tall and the second is .
- One bar looks twice the other, though is nowhere near double .
Answer: it starts at 40, so a gap of 4 looks like double
The picture is not wrong, but it flatters a difference of only .
Traps
- Reading the value from the wrong bar or the wrong axis on a graph. Check the label and the axis carefully before reading off a value.
- Assuming the vertical axis of every graph starts at zero. Check the starting value on the axis before comparing bar heights. It can make a small difference look huge.
- Reading a pie chart slice as a count, the way a bar graph gives one. A slice gives a share. Multiply that share by the total to reach a count.
- Predicting from the last point on the graph on its own. Use the trend across the whole graph, and say how far ahead your prediction holds.
Learn and practise “Read graphs and spot trends” in the app →
Bias, extremes and summaries
Why a big sample can still mislead, and why one huge value can wreck an average.
- population
- Every person or thing the question is about.
- sample
- The smaller group actually asked, standing in for all of them.
- bias
- A push in the way data was gathered that tilts the answer one way.
- error
- A wrong value, from a slip in measuring, asking or writing down.
- extreme value
- A value much larger or much smaller than all the rest.
- summary statistic
- One number that stands for a whole set, like the mean or the median.
Before you believe a set of data, ask where it came from. Who was asked? What is one step on the scale worth? How were the groups made up?
The population is everyone the question is about. The sample is the group actually asked. Reporting a sample as if it were the whole population claims more than the data can carry.
Bias comes from the gathering, not from the numbers. A pushy question, or asking only your friends, tilts the answers before anyone counts. A bigger sample chosen the same way is just as biased.
An error is different. It is one wrong value, from a slip in measuring, asking or writing down. A surprising value may be an error, or it may be real. Check how it was collected before you drop it.
One extreme value drags the mean towards itself, because the mean uses every value. It stretches the range too. The median hardly moves, so it is the better summary statistic here. The mode is no use when every value happens once.
Examples
Worked answer
- Add them: , and .
- Divide by five days: .
- Order them: ; ; ; ; .
- The middle one is .
Answer: mean R802, median R510
The R2 000 school-event day is an extreme value, and it lifts the mean above four of the five days.
Worked answer
- Range: .
- That single number describes the spread, not a typical day.
- A typical day is nearer the median, R510.
- Drop the event day and the range falls to .
Answer: range R1 520, and it says nothing about a typical day
One extreme value changes the range far more than it changes the median.
Worked answer
- The population is everyone she wants as a customer.
- Her sample is only the people the hours already suit.
- Everyone kept away by those hours is left out.
- Asking a hundred more of the same customers will not fix it.
Answer: the sample leaves out the people the hours do not suit
That is bias, and bias comes from who was chosen, not from how many.
Traps
- Assuming one very large or very small value cannot change the mean. The mean uses every value, so one extreme value can pull it a long way.
- Choosing the mean to represent a data set that has an extreme value. When there is an extreme value, the median usually represents the data better than the mean.
- Trusting a large sample without asking how the people in it were chosen. Bias comes from the choosing, not the size. A large biased sample is still biased.
- Saying a table with four groups holds four values. A group can hold many values. Add the counts to find how many there really are.
Learn and practise “Bias, extremes and summaries” in the app →