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[h]SL 4.2 Understanding of box and whisker diagrams
[q] Frequency Table
[a] Instead of a long list of data, it might be more efficient to say how many (the frequency) of each value we have.
[q] Histograms
[a] Similar to a bar chart, but suitable for continuous data as it shows the frequency between various interval.
[q] Quartiles
[a] You will know that the range is a basic measure of each word formed by doing highest value lowest value. However, extreme values can distort this fig, so an alternative is to assess how spread out the central 50% of data is. This is called the interquartile range.
[q] Quartile 1 (Q1)
[a] The value that is \(\frac{1}{4}\) of the way through the ordered data.
[q] Quartile 3 (Q3)
[a] The value that is \(\frac{3}{4}\) of the way through the ordered data.
[q] Interquartile Range (IQR)
[a] \(IQR=Q_{3}-Q_{1}\)
[q] Box and Whisker
[a] We can combine the medain with the quartiles, and extremes to make a diagram that displays the spread. We draw 5 vertical lines for lowest/highest, \(Q_{1}\), \(Q_{3}\) and median, then join with box and whiskers.
[q] Outliers
[a] A point more than 1.5 × IQR below \(Q_{1}\) or above \(Q_{3}\).
[q] Cumulative Frequency Graphs
[a] This is a line graph showing the cumulative frequency (a ‘running total’) of how many data points have occured that are less than a particular ‘x’ value. We plot upper boundary against cumulative frequency.
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