Mathematics·Statistics and probability · NSSCO 12.3
Cumulative frequency & quartiles
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A grouped frequency table hides its story in a pile of numbers. In this lesson we set that story free. We add a running total to make a cumulative frequency table, plot those totals against the upper class boundaries to draw a smooth S-shaped curve (an ogive), then read off the median and the lower and upper quartiles, work out the interquartile range, count how many values fall above or below a mark, find percentiles, and finish by turning our five key numbers into a box-and-whisker plot.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 12.3):
- Build a cumulative frequency table from a grouped frequency table using running totals
- Plot a cumulative frequency curve (ogive) against the upper class boundaries and join with a smooth curve
- Read the median (n/2), lower quartile (n/4) and upper quartile (3n/4) from the curve
- Calculate the interquartile range as upper quartile minus lower quartile
- Estimate how many values fall above or below a given value, and read percentiles from the curve
- Draw and interpret a box-and-whisker plot from the five-number summary
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