Estimating Quantiles of Grouped Discrete Data

Statistics - estimating quantiles of a distribution using linear interpolation

Author and programmer: Ron Barrow

UK Years 12-13, KS5, A Level Statistics


Instructions below See also:   Cumulative Frequency Diagrams

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How to Use this Applet

On the screen you see the data displayed as a frequency table and also as a cumulative frequency table. The cumulative frequency graph is drawn for you, and you can optionally view the frequency graph by checking the "Distribution" box at the bottom. You can click and drag on the little circles on the vertical axis, and this changes the frequencies in the different intervals. Alternatively there are some preset distributions which you can access from the drop down menu "Choose distribution type" at the top of the screen. Clicking and dragging the circle at the left edge changes the percentage point, and a line drawn from this circle leads to the estimated percentile along the horizontal axis. You can vary the interval width by clicking the "Width -" and "Width +" buttons at the bottom. The calculations for the estimate are shown at the bottom right of the screen. By playing around around with the different controls, and looking at the working, you should be able to get a feel for this technique of estimation. The technique uses linear interpolation, which makes the assumption that in each interval there is a linear relationship (i.e. straight line segments on the graph). Play around and learn!