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?
Explain in detail
a) Based on the data provided, an outlier can be identified as the gasoline price in June 2008, which is significantly higher than the surrounding values.
b)
Mean = (80.3 + 102 + 97 + 130.5 + 71 + 86 + 86 + 87.5 + 96.2 + 124 + 98) / 11 = 94.7
Median = The middle value when the data is arranged in ascending order: 86
Mode = The most frequently occurring value: 86
c) In this case, the median value of 86 gives a better measure of central tendency compared to the mean and mode. This is because the mean is affected by outliers, such as the high gasoline price in June 2008, which can skew the average. The mode, while useful for identifying the most frequent value, may not always accurately represent the central tendency of the data set. The median, on the other hand, is not affected by outliers and provides a more representative value of the central tendency of the data set.