Using Statistical Measures to Compare Populations Warm Up

Using Statistical Measures to Compare Populations

Warm Up The tables show the numbers of miles run by the students in two classes. 1. For each class, what is the mean? What is the mean absolute deviation (MAD)? 2. The difference of the means is about _____ times the (MAD).

• To find the mean absolute deviation (MAD) of a data set, find the mean of the data, take the absolute value of the difference between the mean and each data point, and then find the mean of those absolute values. • For any given population, many different random samples are possible, and their measures of center can vary. • Using multiple samples can give an idea of the reliability of any inferences or predictions.

How can you use statistical measures to compare populations? You can compare data sets by finding measures of center and variability. If the variabilities are similar, you can express the difference in centers as a multiple of the variabilities. You can also take multiple samples from populations and compare the distributions of the medians or the means of the samples.

How does the A in MAD help you recall how to calculate the MAD? • The A stands for “absolute. ” One step in finding the MAD is to find the absolute value of the difference between each data value and the mean of the data set. • Not all sets of data being compared will have similar MAD values. Only when the MAD values are nearly the same can the difference of the means as a multiple of the MAD be calculated. • Finding the MAD involves a lengthy series of calculations, and errors can easily sneak in. If you find MADs that are significantly different from each other, you have made an error and need to recalculate.

• The mean absolute deviation (MAD) is the average distance of the data set from its mean. • It is a measure of statistical dispersion of quantitative data. • A data set with a smaller MAD has data values that clustered closer to the mean than a data set with a greater MAD. • This should not be confused with the median absolute deviation, the median of the absolute deviations from the median.

3, 7, 8 • Find the mean of the data set. • Find the distance of each data point from the mean. • Find the mean absolute deviation.

For the data in the table, what is the difference of the means as a multiple of the mean absolute deviation? Describe how you found your answer. What inference could you make? How could you check its reliability?

The test scores of two students are shown below. What is the difference of the means as a multiple of the mean absolute deviation?

• The median is the point through which a vertical line has been drawn for each box plot. • The shape of the box plot is used to visualize whether the data values are evenly distributed (the whiskers and the two parts of the box will be about the same length) or grouped more on one side of the median. • Five key values shown in every box plot are the upper and lower extremes, upper and lower quartiles, and the median.

A group of 300 students in Grade 8 and 300 in Grade 12 were asked, “On average, how many text messages do you receive or send each day? ” The box plot below shows the means from 10 different random samples of size 10. Compare the number of text messages for the two populations.

How do you use the mean to find the difference of two sets of data as a multiple of the MAD? First, find the mean and the MAD of both sets of data. Then, if the MADs of both sets are similar, divide the difference of the two means by the MAD.

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