The table gives the six-month average gasoline prices in Calgary for the period of December 2006 to December 2011. Use the information in the table to answer the following questions
Calgary Gas Prices December 2006 το 2011
Month/year. Price
December 2006. 80.3
June 2007. 102
December 2007. 97
June 2008. 130.5
December 2008. 71
June 2009. 86
December 2009. 86
June 2010. 87.5
December 2010. 96.2
June 2011. 124
December 2011. 98
b) Find the mean, median, and mode and compare the measures.
c) Which value gives the best measure of central tendency? Why?
b)
Mean: To find the mean, add up all the prices and divide by the number of prices:
(80.3 + 102 + 97 + 130.5 + 71 + 86 + 86 + 87.5 + 96.2 + 124 + 98) / 11 = 96.3
Median: To find the median, arrange the prices in numerical order and find the middle value:
71, 80.3, 86, 86, 87.5, 96.2, 97, 98, 102, 124, 130.5
Median = 96.2
Mode: The mode is the number that appears most frequently in the data set. In this case, the mode is 86 as it appears twice.
c) The best measure of central tendency in this case would be the median. The mean can sometimes be skewed by extreme values (like the high prices in June 2008 and June 2011), so the median, which is not influenced by extreme values, gives a better representation of the central tendency of the gas prices over the period. The mode, while useful for identifying the most common value, may not provide a good representation of the overall data set.