Questions: Compare the three data sets on the right. (i) (ii) (iii) (a) Which data set has the greatest sample standard deviation? A. Data set (iii), because it contains the greater number of entries. B. Data set (ii), because it has more entries that are farther away from the mean. C. Data set (i), because its data have more variability. Which data set has the least sample standard deviation? A. Data set (i) because it has more entries near the mean than far away from it. B. Data set (iii), because it has more entries that are close to the mean. C. Data set (ii), because it has no entries near the mean.

Compare the three data sets on the right. (i) (ii) (iii) (a) Which data set has the greatest sample standard deviation? A. Data set (iii), because it contains the greater number of entries. B. Data set (ii), because it has more entries that are farther away from the mean. C. Data set (i), because its data have more variability. Which data set has the least sample standard deviation? A. Data set (i) because it has more entries near the mean than far away from it. B. Data set (iii), because it has more entries that are close to the mean. C. Data set (ii), because it has no entries near the mean.
Transcript text: Compare the three data sets on the right. (i) (ii) (iii) (a) Which data set has the greatest sample standard deviation? A. Data set (iii), because it contains the greater number of entries. B. Data set (ii), because it has more entries that are farther away from the mean. C. Data set (i), because its data have more variability. Which data set has the least sample standard deviation? A. Data set (i) because it has more entries near the mean than far away from it. B. Data set (iii), because it has more entries that are close to the mean. C. Data set (ii), because it has no entries near the mean.
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Solution

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Solution Steps

Step 1: Identify the data sets
  • There are three data sets labeled (i), (ii), and (iii) shown in the histograms.
Step 2: Determine the greatest sample standard deviation
  • The sample standard deviation measures the spread of data points from the mean.
  • Data set (ii) has more entries that are farther away from the mean, indicating a larger spread.

Final Answer

  • (a) Data set (ii), because it has more entries that are farther away from the mean.
Step 3: Determine the least sample standard deviation
  • The least sample standard deviation will be for the data set with entries closest to the mean.
  • Data set (i) has more entries near the mean than far away from it.
Final Answer
  • Data set (i) because it has more entries near the mean than far away from it.
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