Over the first five years of owning a car, Gina drove about 12,700 miles the first year, 15,478 miles the second year, 12,675 the third year, 11,850 the fourth year, and 13,075 the fifth year.
a. Find the mean, median, and mode of this data.
b. Explain which measure of central tendency will best predict how many miles Gina will drive in the sixth year.
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a.
Mean:
Add up all the miles driven over the five years:
12,700 + 15,478 + 12,675 + 11,850 + 13,075 = 65,778
Divide by the total number of years (5) to find the mean:
65,778 / 5 = 13,155.6
Median:
Arrange the miles driven in ascending order:
11,850, 12,675, 12,700, 13,075, 15,478
The middle value is the median:
Median = 12,700
Mode:
The mode is the value that appears most frequently. None of the values in this data set appear more than once, so there is no mode.
b.
Since Gina has driven various mileages over the past five years, it may be difficult to predict how many miles she will drive in the sixth year with certainty. However, the measure of central tendency that would best predict her mileage in the sixth year is likely the mean. This is because the mean takes into consideration all values and provides an average, which can be a good indicator of a typical amount.