~ 8.15 ~

Estimating Populations Measures of Center

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Learning Targets

I can consider the variability of a sample to get an idea for how accurate my estimate is.
I can estimate the mean or median of a population based on a sample of the population.

Notes

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:

Mean weight: 12.8 kg
MAD: 2.3 kg

Beagle meetup:

Mean weight: 10.1 kg
MAD: 0.8 kg

The lower MAD indicates 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, a sample of a similar size from a population with less variability is more likely to have a mean that is close to the population mean.

Activities

15.1 Describing the Center

Would you use the median or mean to describe the center of each data set? Explain your reasoning.

1. Heights of 50 basketball players

2. Ages of 30 people at a family dinner party

3. Backpack weights of sixth-grade students

4. How many books students read over summer break

15.4 Movie Reviews

A movie rating website has many people rate a new movie on a scale of 0 to 100. Here is a dot plot showing a random sample of 20 of these reviews.

Would the mean or median be a better measure for the center of this data? Explain your reasoning.
Use the sample to estimate the measure of center that you chose for all the reviews.
For this sample, the mean absolute deviation is 19.6, and the interquartile range is 15. Which of these values is associated with the measure of center that you chose?
Movies must have an average rating of 75 or more from all the reviews on the website to be considered for an award. Do you think this movie will be considered for the award? Use the measure of center and measure of variability that you chose to justify your answer.

Add to Your Notes

How do you determine which measure of center will be best describe the data in a sample?

Base it on the distribution of the data.

When you have the data from a sample, how can you estimate the value of a measure of center for the population?

If the sample is random, calculate the appropriate measure of center for the sample and use that to estimate the same characteristic for the popultion.

What does the variability of the sample tell you about your estimate for the measure of center of the population?

The greater the variability, the less certain we can be of the estimate.

15.5 More Accurate Estimate

Each dot plot represents a sample of 100 data.

Estimate the population means using these samples.
Based on the dot plots, which estimate is more likely to be accurate? Explain your reasoning.

Sample 1:

Sample 2:

Assignment

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