Math 6 B: Measures of Variation Practice -Google Chrome answers
1. What is the range of the data set: 10, 15, 20, 25, 30?
The range is 20 (30 - 10).
2. Calculate the interquartile range for the following data set: 5, 10, 15, 20, 25, 30, 35, 40.
First, find the median (it is 22.5). Then, find the median of the lower half (the lower quartile = 10 + 15 = 12.5) and the upper half (the upper quartile = 30 + 35 = 32.5). The interquartile range is 32.5 - 12.5 = 20.
3. Find the standard deviation of the data set: 2, 4, 6, 8, 10.
First, find the mean (the mean is 6). Then, find the squared differences from the mean: (6-2)^2 + (6-4)^2 + (6-6)^2 + (6-8)^2 + (6-10)^2 = 4 + 4 + 0 + 4 + 16 = 28. Next, divide by the number of values (5) and take the square root, so sqrt(28/5) = sqrt(5.6) ≈ 2.37.
4. Find the variance of the data set: 3, 6, 9, 12, 15.
First, find the mean (the mean is 9). Next, find the squared differences from the mean: (9-3)^2 + (9-6)^2 + (9-9)^2 + (9-12)^2 + (9-15)^2 = 36 + 9 + 0 + 9 + 36 = 90. Then, divide by the number of values (5), so 90/5 = 18.
5. Calculate the mean absolute deviation of the data set: 4, 7, 9, 12, 17.
First, find the mean (the mean is 9.8). Next, find the absolute differences from the mean: |4-9.8| + |7-9.8| + |9-9.8| + |12-9.8| + |17-9.8| = 5.8 + 2.8 + 0.8 + 2.2 + 7.2 = 18.8. Then, divide by the number of values (5), so 18.8/5 = 3.76.