Samples and means

What it does
Samples and means
provides an environment in which some of the big ideas of statistical sampling can be explored, such as:
–the idea of “deviation" (d) about a fixed point (for example about the sample mean or about the population mean);
–the idea of a “squared deviation" (d-squared) about a fixed point;
–the mean, variance and standard deviation;
–how sample size influences how closely a sample mean lies to the population mean;
–and much more.

Settings and tools
Random selection is first opened, you see a screen similar to the one shown opposite. The settings and tools are as follows:
sample size: select any value from 1 to 20.
next sample: a new sample is generated each time this button is clicked.
distribution of population: select between uniform and normal.
deviations from: select the fixed point about which the deviations are calculated (choose from sample mean, population mean, or any integer value from 0 to 10).
show: click this to see, on a separate window, the means of the square deviations calculated about all the integer values from 0 to 10.

The displays are as follows
–current sample values are displayed as a.plot at the top of the screen;
–the positions of the sample mean (orange bar) and population mean (green bar) are are indicated on the dot plot; additionally, when one of the integer values is selected from the “deviations from" menu, its position is also displayed (blue bar) on the dot plot;
–all sample deviations, d, are shown visually below the dotplot; negative deviations are shown in red and positive deviations in blue;
–the d and d-squared values are displayed on the right of the screen, along with the sum of the squared deviations, the variance and the standard deviation.

Screenshot of Samples and means

Stacks Image 520

There are ten movies linked to this applet:

Go to '
A ten-lesson course on sampling'.

Run the applet Samples and means