Suppose you use a graphing calculator to generate a table of summary statistics for two data sets, A and B. Data set A has a mean of $50$ and a standard deviation of $5$, while data set B has a mean of $50$ and a standard deviation of $15$. Which generalization is most accurate based on these statistics?

• A. Data set A and data set B have the same variability.
• B. Data set B is less variable than data set A.
• C. Data set B is more spread out around the mean than data set A.
• D. Data set A has a higher mean than data set B.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the meaning of the mean and standard deviation. The mean represents the average value of the data set, while the standard deviation measures how spread out the data values are around the mean.
2. Step 2: Compare the means of data sets A and B. Both have the same mean of 50, so their central tendency (average) is identical.
3. Step 3: Compare the standard deviations of data sets A and B. Data set A has a standard deviation of 5, and data set B has a standard deviation of 15. Since standard deviation quantifies variability, a larger standard deviation means more spread out data.
4. Step 4: Interpret the comparison. Because 15 is greater than 5, data set B is more spread out around the mean than data set A, indicating greater variability in data set B.
5. Step 5: Conclude which generalization is most accurate. Since the means are equal but the standard deviations differ, the statement 'Data set B is more spread out around the mean than data set A' best describes the relationship between the two data sets.