Measures of Dispersion - SS2 Economics Past Questions and Answers - page 1
Which of the following measures of dispersion is calculated by subtracting the smallest value from the largest value in a dataset?
Variance
Standard deviation
Range
Mean
Which of the following measures of dispersion gives an idea of how much the data is spread out around the mean?
Range
Variance
Standard deviation
Median
Which of the following measures of dispersion is sensitive to outliers?
Range
Variance
Standard deviation
Mean
Which of the following measures of dispersion is always positive or zero?
Range
Variance
Standard deviation
Mean
Which of the following measures of dispersion is useful in identifying extreme values or outliers?
Range
Variance
Standard deviation
Mean
The heights (in inches) of a group of basketball players are 71, 74, 68, 72, 70, and 75. What is the range of the players' heights?
The smallest height is 68 inches, and the largest height is 75 inches. Therefore, the range is 75 - 68 = 7 inches.
The weights (in pounds) of a group of people are 150, 140, 165, 180, 130, and 170. What is the standard deviation of the weights?
From the previous example, we know that the variance is 791.25. Therefore, the standard deviation is the square root of 791.25, which is approximately 28.11.
The weights (in pounds) of a group of people are 150, 140, 165, 180, 130, and 170. What is the variance of the weights?
The mean weight is (150+140+165+180+130+170)/6 = 157.5
The squared differences between each weight and the mean are: (150-157.5)², (140-157.5)², (165-157.5)², (180-157.5)², (130-157.5)², and (170-157.5)²
The average of these squared differences is (49.5² + 17.5² + 7.5² + 506.252 + 688.522+ 12.5²)/6 = 791.25.
Therefore, the variance is 791.25.