Question

1. the mean of data set a is 43.5 and the mad is 3.7. the mean of data set b is 12.8 and the mad is 4.1. (lesson 1 - 11)

a. which data set shows greater variability? explain your reasoning.
b. what differences would you expect to see when comparing the dot plots of the two data sets?

Explanation:

Step1: Recall the concept of MAD (Mean Absolute Deviation)

MAD measures the variability of a data - set. A larger MAD indicates greater variability.

Step2: Compare the MADs of data set A and data set B

Data set A has a MAD of \(4.1\) and data set B has a MAD of \(3.7\). Since \(4.1>3.7\), data set A has greater variability.

Step3: Analyze the dot - plots based on variability

A data set with greater variability (higher MAD) will have data points more spread out from the mean. So, when comparing the dot - plots, the dot - plot of data set A will have data points more spread out around its mean (\(43.5\)) compared to the dot - plot of data set B (with mean \(12.8\))

Answer:

a. Data set A shows greater variability. Because the MAD (Mean Absolute Deviation) of data set A (\(4.1\)) is greater than the MAD of data set B (\(3.7\)), and a larger MAD implies more variability in the data.
b. The dot - plot of data set A would have data points more spread out around its mean (\(43.5\)) compared to the dot - plot of data set B (around its mean \(12.8\)) as data set A has higher variability (due to its larger MAD).