Students keep making the same mistakes in their GCSE Maths exams. Inspired by the examiner's reports find out where students are losing vital marks, so that you can avoid the common slip-ups!
Graphs and Charts 2
1. Cumulative Frequency simply means adding the frequencies up as you go along.
2. When plotting the graph, always plot points using the upper value of each group.
3. Cumulative frequency is always plotted on the vertical axis (up the side) and the range of data goes across the bottom.
4. The shape of a cumulative frequency curve looks like a 'stretched S' and is called an ogive.
5. The more "stretched-out" the 'S' the more spread out is the data. An 'S' with a very steep middle section indicates the data being tightly grouped around the median. (See diagram below):
Black line = Very tight distribution grouped around the median.
Red line = Much more widely spread distribution. Large interquartile range.
A Cumulative Frequency graph is used to provide estimates of the median (and quartiles) when the data is grouped. (Remember that with grouped data you cannot say what the Median is, only which group it is in!)
We can get 4 main pieces of information from a Cumulative Frequency graph:
1. Median - go halfway up the cumulative frequency axis, read across and down then read the median from the bottom scale.
2. Lower Quartile - go a quarter of the way up the cumulative frequency axis, read across and down then read the Lower Quartile from the bottom scale.
3. Upper Quartile - go three-quarters of the way up the cumulative frequency axis, read across and down then read the Upper Quartile from the bottom scale.
4. Inter-Quartile Range - the difference between the Lower Quartile and the Upper Quartile.
Can you remember all that? Test yourself by dragging in the correct words on to the question marks in the panels below. Then mark your answer:
To see what we mean, have a look at the following example...
A zookeeper measures the lengths of all the snakes in a zoo and records the results in a table:
He then constructs the following Cumulative Frequency graph and reads the Median, Lower and Upper Quartiles and finds the Inter-Quartile Range.
See if you can construct a Cumulative Frequency graph in the same way using the table below which shows the weights of pupils in a year-group.
Type in the Cumulative Frequency in the dark blues boxes and click Mark Answer to see if your are correct: