Range and standard deviation
Comparing Range and Standard Deviation
Which of the following statements correctly compares the ranges and standard deviations of data set A and data set B, that are represented by the dot plots above?
Solution:
In data set A, the greatest value is and the smallest value is . Hence, the range of data set A is . Similarly, in data set B, the greatest value is and the smallest value is . Hence, the range of data set B is . Thus, the range of data set A is greater than the range of data set B.
We can see that the values of data set B are more concentrated near the mean, and the values of data set A are more spread out. Hence, the standard deviation of data set A is greater than the standard deviation of data set B.
The range of data set A is greater than the range of data set B, and the standard deviation of data set A is greater than the standard deviation of data set B.