Spread and standard deviation Problem set A Answers

MAD = 3.2

1. (a) Variance = 13.2
2. (b) σ = 3.63

1. (a) Mean = 31
2. (b) Sum of squared deviations = 206
3. (c) σ = 6.42

1. (a) Both means are 10
2. (b) Route 1: σ = 1.12. Route 2: σ = 3.74
3. (c) Route 2, because its standard deviation is larger

1. (a) 68%
2. (b) 95%
3. (c) 0.15%

1. (a) Mean = 43
2. (b) σ = 2.45
3. (c) 4.49 standard deviations above the mean

1. (a) Mean = 17, σ = 3.29
2. (b) Mean = 25, σ = 3.29
3. (c) Mean = 34, σ = 6.57
4. (d) Adding 8 to every value adds 8 to the mean and leaves the standard deviation the same. Multiplying every value by 2 multiplies both the mean and the standard deviation by 2.

1. (a) Mean = 4.9, σ = 0.433
2. (b) Mean = 11.2, σ = 16.9
3. (c) Correct: median = 4.9, IQR = 0.7. With the error: median = 4.9, IQR = 0.7
4. (d) The mean and standard deviation change a lot; the median and IQR do not. With an extreme value, use the median and IQR.

1. (a) Both means are 500; both MADs are 2.4
2. (b) Machine 1: σ = 2.83. Machine 2: σ = 3.79
3. (c) Machine 1, because its standard deviation is smaller

1. (a) About 136
2. (b) About 5
3. (c) 54 to 86