Given Q1 = 10, Q3 = 20, IQR = 10, which value would be considered an outlier under the IQR rule?

Given Q1 = 10, Q3 = 20, IQR = 10, which value would be considered an outlier under the IQR rule?

• A. 0
• B. 12
• C. -6
• D. 30

Answer: (C)

The IQR rule flags values outside 1.5 times the IQR beyond the quartiles as outliers. With Q1 = 10, Q3 = 20, and IQR = 10, the fences are: lower bound = Q1 − 1.5×IQR = 10 − 15 = −5 upper bound = Q3 + 1.5×IQR = 20 + 15 = 35 So any value below −5 or above 35 is an outlier. Among the options, −6 is below −5, making it an outlier. The others (0, 12, 30) all lie within [−5, 35], so they are not outliers.

The IQR rule flags values outside 1.5 times the IQR beyond the quartiles as outliers. With Q1 = 10, Q3 = 20, and IQR = 10, the fences are:

lower bound = Q1 − 1.5×IQR = 10 − 15 = −5

upper bound = Q3 + 1.5×IQR = 20 + 15 = 35

So any value below −5 or above 35 is an outlier. Among the options, −6 is below −5, making it an outlier. The others (0, 12, 30) all lie within [−5, 35], so they are not outliers.