#### 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

When 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

**There are ten movies linked to this applet:Go to '**

**A ten-lesson course on sampling**

**'.**

**Run the applet ****Samples and means**