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
a) Are there any outliers? If so, what are they?
b) Find the mean, median, and mode and compare the measures.
c) Which value gives the best measure of central tendency? Why?
a) Yes, there are outliers in the data set. The outlier is the price of 130.5 in June 2008, which is significantly higher than the other values in the data set.
b) Mean:
(80.3 + 102 + 97 + 130.5 + 71 + 86 + 86 + 87.5 + 96.2 + 124 + 98) / 11 = 96.59
Median:
Arranging the prices in ascending order:
71, 80.3, 86, 86, 87.5, 96.2, 97, 98, 102, 124, 130.5
Median = 96.2
Mode:
The mode is the value that appears most frequently in the data set. In this case, there is no mode as each price appears only once.
c) In this case, the median gives the best measure of central tendency. This is because the data set contains an outlier (130.5), which significantly affects the mean. The median, being the middle value when the data is arranged in order, is not affected by outliers and provides a more representative measure of central tendency in this scenario.