Spread and standard deviation Problem set B Answers

MAD = 4.4

1. (a) Variance = 14.4
2. (b) σ = 3.79

1. (a) Mean = 52
2. (b) Sum of squared deviations = 266
3. (c) σ = 7.29

1. (a) Both means are 500
2. (b) Bakery 1: σ = 1.80. Bakery 2: σ = 5.61
3. (c) Bakery 2, because its standard deviation is larger

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

1. (a) Mean = 61
2. (b) σ = 2.37
3. (c) 2.96 standard deviations below the mean

1. (a) Mean = 25, σ = 5.02
2. (b) Mean = 31, σ = 5.02
3. (c) Mean = 50, σ = 10.0
4. (d) Adding 6 to every value adds 6 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 = 36.5, σ = 3.5
2. (b) Mean = 83.8, σ = 127
3. (c) Correct: median = 36.5, IQR = 6. With the error: median = 36.5, IQR = 6
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 40; both MADs are 1.6
2. (b) Baker 1: σ = 2. Baker 2: σ = 2.53
3. (c) Baker 1, because its standard deviation is smaller

1. (a) About 272
2. (b) About 10
3. (c) 102 to 138