Question

1. the mean of data set a is 43.5 and the standard deviation is 7.4. the mean of data set b is 12.8 and the standard deviation is 4.1

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 variability measure

Standard - deviation measures data - set variability. Larger standard - deviation means more variability.

Step2: Compare standard deviations

Data set A has standard deviation 7.4 and data set B has standard deviation 4.1. Since 7.4>4.1, data set A has greater variability.

Step3: Analyze dot - plot differences

For the dot - plots, data set A will have data points more spread out around the mean (43.5) compared to data set B which has data points more clustered around the mean (12.8) because of its smaller standard deviation.

Answer:

a) Data set A shows greater variability because its standard deviation (7.4) is larger than the standard deviation of data set B (4.1).
b) The dot - plot of data set A will have data points more spread out around the mean of 43.5, while the dot - plot of data set B will have data points more clustered around the mean of 12.8.