Estimating Population Measures of Center

Student Summary

Some populations have greater variability than others. For example, we would expect greater variability in the weights of dogs at a dog park than at a beagle meetup.

Dog park:

A picture of 2 small dogs, 2 medium sized dogs, and 3 large dogs.

Mean weight: 12.8 kg       MAD: 2.3 kg

Beagle meetup:

A picture of 7 similar sized beagle dogs.

Mean weight: 10.1 kg       MAD: 0.8 kg

The lower MAD indicates that there is less variability in the weights of the beagles. We would expect that the mean weight from a sample that is randomly selected from a group of beagles will provide a more accurate estimate of the mean weight of all the beagles than a sample of the same size from the dogs at the dog park.

In general, if samples from a population have similar sizes, a sample with less variability is more likely to have a mean that is close to the population mean.

Visual / Anchor Chart

Standards

Building On
6.SP.5.d

Summarize quantitative data sets in relation to their context.

Addressing
7.SP.1

Construct and interpret box-plots, find the interquartile range, and determine if a data point is an outlier.

7.SP.2

No additional information available.

7.SP.4

Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations.

Building Toward
7.SP.2

No additional information available.

7.SP.4

Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations.