The range would best describe the spread of this data set because it gives a complete picture of the variability in the data.
To calculate the range, we subtract the smallest value from the largest value:
18.0 - 11.0 = 7.0
This means that the range of the data set is 7.0 seconds.
To identify outliers, we can calculate the Interquartile Range (IQR) and look for values that fall significantly above or below the upper and lower quartiles.
To calculate the IQR:
1. Arrange the data in ascending order:
11.0 11.2 11.7 12.2 12.4 12.6 12.8 12.9 13.1 13.3 13.8 14.2 14.3 14.3 16.5 17.6 18.0
2. Calculate the first quartile (Q1) and the third quartile (Q3):
Q1 = 12.8
Q3 = 14.3
3. Calculate the IQR:
IQR = Q3 - Q1
IQR = 14.3 - 12.8
IQR = 1.5
Any value that falls more than 1.5 times the IQR below Q1 or above Q3 could be considered an outlier. In this case, there are no values that fall outside that range, so there are no outliers in this data set.
Determine whether the range or interquartile the Range best describes the spread of a data set and any outliers.
The Times (In seconds) For a high school boys’ 100 meter race:
11.0 11.2 11.7 12.2 12.4 12.6 12.8 12.9 13.1 13.3 13.8 14.2 14.3 14.3 16.5 17.6 18.0
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