2.36 Who Is Paying More at the Pump? The prices below are for regular gasoline (per litre) as of December 29, 2011.

a. Find the standard deviation of these values.

b. Find the range R. Compare the range and the standard deviation. Is range related to standard deviation, in any sense?

c. Use range to approximate the standard deviation. Is this a good approximation?

d. Subtract 0.5 from every observation and calculate the variance for the original data and the new data. What effect, if any, does subtracting 0.5 from every observation have on the sample variance?

e. What percentage of the measurements will lie within three standard deviations of the overall mean? Does the result agree with Tchebysheff's Theorem?

f. Find the percentage of measurements in the inter- valss and 2s. Compare these results with the Empirical Rule percentages, and comment on the shape of the distribution. g. In how many provinces is the average gas price stabilized?

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Area Price per Litre ($) Alberta Ontario 101.108 119.602 New Brunswick Manitoba 121.877 109.853 Quebec 128.760 Nova Scotia 122.700 Saskatchewan 115.118 British Columbia 123.150 Newfoundland and Labrador 128.923 Source: Data provided by GasBuddy.com