4 Compare the () 7 7 three data sets on the right. 1011 34567891011 456 Data val

Question

4 Compare the () 7 7 three data sets on the right. 1011 34567891011 456 Data value 345 891011 Data value Data value d25 d36 (a) Which data set has the greatest sample standard deviation? O A. Data set (i), because it has more entries that are farther away from the mean. O B. Data set (ii), because it contains the greater number of entries. OC. Data set (ii), because its data have more variability. Which data set has the least sample standard deviation? O A. Data set (iii) because it has more entries near the mean than far away from it. O B. Data set (i), because it has no entries near the mean. O C. Data set (i), because it has more entries that are close to the mean. (b) How are the data sets the same? How do they differ? O A. The three data sets have the same range but have different means. OB. The three data sets have the same standard deviations but have different ranges. The three data sets have the same range and mean but have different standard deviations. same mean but have different standard deviations.

Explanation / Answer

a) Since the histogram i has more values to the extreme side, this would be the data set with highest standard deviation.

Option A is correct.

Since the histogram ii has values concentrated to the middle, this would be the data set with least standard deviation.

Option C is correct.

b) The three data sets are having the same mean i.e. 7 but different standard deviations.

Option D is correct.

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