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.
Explain in detail
To find the mean, median, and mode of the gasoline prices in Calgary from December 2006 to December 2011, we first need to calculate the average price for each year. Then we can find the mean, median, and mode of these average prices.
1. Calculate the average price for each year:
- 2006: (80.3 + 102) / 2 = 91.15
- 2007: (102 + 97) / 2 = 99.5
- 2008: (97 + 130.5) / 2 = 113.75
- 2009: (130.5 + 86) / 2 = 108.25
- 2010: (86 + 87.5) / 2 = 86.75
- 2011: (87.5 + 98) / 2 = 92.75
2. Find the mean:
Mean = (91.15 + 99.5 + 113.75 + 108.25 + 86.75 + 92.75) / 6 = 99.91
3. Find the median:
We arrange the average prices in ascending order: 86.75, 91.15, 92.75, 99.5, 108.25, 113.75
Since we have an even number of values, the median is the average of the two middle values:
Median = (92.75 + 99.5) / 2 = 96.13
4. Find the mode:
The mode is the value that appears most frequently in the data set. In this case, the mode is 86.75 as it appears twice in the data set, which is more frequent than any other value.
Comparison of the measures:
- The mean is 99.91, which is the average of all average prices over the years.
- The median is 96.13, which is the middle value of the ordered set of average prices.
- The mode is 86.75, which is the value that appears most frequently in the data set.
In this case, the mean, median, and mode are relatively close to each other, suggesting that the data set is approximately symmetric and does not have any significant outliers affecting the measures.