The five number summary of a dataset was found to be: $46,51,59,64,70$ An observation is considered an outlier if it is below: An observation is considered an outlier if it is above:
Solution
Step 1 ：The five number summary of a dataset includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. In this case, these are given as 46, 51, 59, 64, and 70 respectively.
Step 2 ：To determine if an observation is an outlier, we use the Interquartile Range (IQR), which is calculated as Q3 - Q1. In this case, Q3 is 64 and Q1 is 51, so the IQR is 13.
Step 3 ：An observation is considered an outlier if it is below Q1 - 1.5*IQR or above Q3 + 1.5*IQR. Therefore, we calculate these values.
Step 4 ：First, calculate Q1 - 1.5*IQR: 51 - 1.5*13 = 31.5. This is the lower bound for outliers.
Step 5 ：Next, calculate Q3 + 1.5*IQR: 64 + 1.5*13 = 83.5. This is the upper bound for outliers.
Step 6 ：Final Answer: An observation is considered an outlier if it is below \(\boxed{31.5}\) or above \(\boxed{83.5}\).
