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AQA A Level Maths: Statistics復(fù)習(xí)筆記2.2.2 Box Plots & Cumulative Frequency

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月9日下午3:49

What is a box plot?

A box plot is a graph that clearly shows key statistics from a data set
- It shows the?median, quartiles, minimum?and?maximum values?and?outliers
- It does not show any other individual data items
The middle 50% of the data will be represented by the box section of the graph and the lower and upper 25% of the data will be represented by each of the whiskers
Any outliers are represented with a cross?on the outside of the whiskers
- If there is an outlier then the whisker will end at the value before the outlier
Only one axis is used when graphing a box plot
- It is still important to make sure the axis has a clear, even scale and is labelled with units
Box plots are often used for comparing two sets of data
- Both box plots will be drawn one above the other on the same scale on the x-axis
- They are useful for?comparing data?because it is easy to see the main shape of the distribution of the data from a box plot

2-2-2-box-plot-diagram-1

The key features of a box plot

The incomplete box plot below shows the tail lengths in cm of some students’ pets.

2-2-2-box-plot-we-diagram

(i)Given that the median tail length was 21 cm, complete the box plot.

(ii)Find the range and interquartile range of the tail lengths.

2-2-2-box-plot-we-solution-part-1

2-2-2-box-plot-we-solution-part-2

Remember a box plot is a graph and should be treated like one, even though there is only one axis. It should have a title, a clear, even scale that is labelled with units if there are any. If drawing two box plots on the same axis label each one clearly.

A cumulative frequency graph is used with data that has been organised into a?grouped frequency?table
The cumulative frequency graph can be used to find estimates of percentiles and quartiles
- As the data is grouped, it is not possible to find the actual values of these statistics

A cumulative frequency graph considers how much data there is up to a certain value, including the data in that group and the one below
Cumulative frequency will always be plotted on the y – axis
- Consider the scale carefully because this will usually be a large number
- You may be asked to add to one or both axes, remember to label both axes clearly and include units on the x – axis if they are needed
The cumulative frequency is calculated by adding the frequency in each group, or class, to the frequency in the ones before
- This is essentially accumulating the frequencies as you go
The cumulative frequency for each class must be plotted against the?upper boundary?of each corresponding class
- The cumulative frequency that corresponds with each upper boundary will not only consider the frequency of the data in that class, but all of the data in the groups below it too
When the points have been plotted they should be joined up with a smooth curve
- However, some may be joined with straight lines from point to point

2-2-2-cumulative-frequency-we-diagram-2-part-1

2-2-2-cumulative-frequency-we-diagram-2-part-2

If you are asked to read values from your graph make sure you use a ruler and mark the lines on clearly to show where you took your readings from. Remember that the graph shows the accumulated frequencies so if you need only the frequency you may need to subtract the previous value.

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