To determine if there are any outliers in a distribution, we can use the interquartile range (IQR) method. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
IQR = Q3 - Q1
In this case, the first quartile (Q1) is 12 and the third quartile (Q3) is 16. Therefore, the IQR is:
IQR = 16 - 12
= 4
To identify outliers, we can use the following rule: any value that is more than 1.5 times the IQR below Q1 or above Q3 is considered an outlier.
In this case, the lower bound for outliers is Q1 - 1.5 * IQR and the upper bound for outliers is Q3 + 1.5 * IQR.
Lower bound = 12 - 1.5 * 4
= 12 - 6
= 6
Upper bound = 16 + 1.5 * 4
= 16 + 6
= 22
Since the minimum value is 3 and the maximum value is 20, neither of them fall outside the lower and upper bounds. Therefore, there are no outliers for this distribution.
Hence, the correct statement is: There are no outliers for this distribution.