Question 1196754: The average finishing time for the 2013 Fox Cities Marathon was 265 minutes and the standard deviation was 55 minutes.
If a timing error at the 2013 Fox Cities Marathon resulted in all times being reported exactly 2 minutes slower than they should have been, which of the following race statistics would change upon the error's correction? Select all that apply.
Group of answer choices
Mean
iqr
Median
Standard Deviation
Range
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answers:
Mean
Median
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Reason:
Consider the set {3,4,5,6,12}
The mean is (3+4+5+6+12)/5 = 6 and the median is 5 since it's the middle-most item.
Now subtract 2 from each item
We'll end up with {1,2,3,4,10} after doing so
The mean is now (1+2+3+4+10)/5 = 4 and the median is 3 since it's the middle-most item.
We see that the mean has also dropped by 2 (since it went from 6 to 4). The same goes for the median (it went from 5 to 3).
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Q1 = first quartile = lower quartile
Q3 = third quartile = upper quartile
IQR = interquartile range
IQR = distance from Q1 to Q3
The IQR of {3,4,5,6,12} is 6-4 = 2 which is the difference of Q1 = 4 and Q3 = 6.
The IQR of {1,2,3,4,10} is 4-2 = 2 and we can see the IQR has not changed. The IQR is one measure of spread. The data set won't get more spread out, or more condensed, if we subtract the same item from each value. The entire set shifts the same amount which will preserve the spread.
The range of {3,4,5,6,12} is max - min = 12-3 = 9
The range of {1,2,3,4,10} is max - min = 10-1 = 9
The range is another measure of spread, and it doesn't change either when we shift the set around.
I recommend plotting the values {3,4,5,6,12} on the number line. Then shifting everything 2 units to the left. I hope you agree that the spread has not been affected.
Since standard deviation is yet another measure of how spread out a data set is, this means the standard deviation will not be affected either. The process of calculating the standard deviation is a bit complicated, so I recommend using a calculator for this part.
Using a calculator shows that...- Population standard deviation of {3,4,5,6,12} is roughly 3.162
- Population standard deviation of {1,2,3,4,10} is roughly 3.162
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In summary, only the mean and median are changed when we subtract 2 from each value. The IQR, standard deviation, and range are not affected.
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