Fuel consumption is commonly measured in miles per gallon (ml/gal). An agency de

Question

Fuel consumption is commonly measured in miles per gallon (ml/gal). An agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. Find the range, variance, and standard deviation for the sample data. Is the decrease of 4 ml/gal unusual? Why or why not? 2 2 2 2 3 2 4 1 2 2 2 3 1 2 2 2 1 2 2 2 0. The range the sample data is ml/gal. (Type an integer or a decimal.) The variance of the sample data is (Round to one decimal place as needed.) The standard deviation of the sample data is ml/gal. (Round to one decimal place as needed.) Is the largest decrease, 4 ml/gal, unusual? Why or why not?

Explanation / Answer

(a) Range = 3

(b) Variance = 0.5

(c) Standard deviation = 0.7

(d) No, it is not unusual.

x d = x - x-bar d^2 2 -0.05 0.0025 2 -0.05 0.0025 2 -0.05 0.0025 2 -0.05 0.0025 3 0.95 0.9025 2 -0.05 0.0025 4 1.95 3.8025 1 -1.05 1.1025 2 -0.05 0.0025 2 -0.05 0.0025 2 -0.05 0.0025 3 0.95 0.9025 1 -1.05 1.1025 2 -0.05 0.0025 2 -0.05 0.0025 2 -0.05 0.0025 1 -1.05 1.1025 2 -0.05 0.0025 2 -0.05 0.0025 2 -0.05 0.0025 N = 20 Range = Max value - Min value = 3 Median = Middle value = 2 Mode = Most frequenct value = 2 = 41 8.95 Mean, x-bar = x /N = 2.05 Variance, s^2 (Sample) = d^2 /(N - 1) = 0.47 SD, s (Sample) = (Sample variance) = 0.69

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