3) find the outlier of the data set. 44, 67, 52, 72, 82, 55, 70, 200, 55, 57, 68
3) find the outlier of the data set. 44, 67, 52, 72, 82, 55, 70, 200, 55, 57, 68
Answer
Explanation:
Step1: Arrange data in ascending order
$44, 52, 55, 55, 57, 67, 68, 70, 72, 82, 200$
Step2: Calculate quartiles
The median (Q2) of the whole data - set is the 6th value when ordered. So Q2 = 67. The lower half of the data is $44, 52, 55, 55, 57$. The median of the lower half (Q1) is 55. The upper half of the data is $68, 70, 72, 82, 200$. The median of the upper half (Q3) is 72.
Step3: Calculate the inter - quartile range (IQR)
$IQR=Q3 - Q1=72 - 55 = 17$
Step4: Determine the boundaries for outliers
The lower boundary for non - outliers is $Q1-1.5\times IQR=55-1.5\times17=55 - 25.5 = 29.5$ The upper boundary for non - outliers is $Q3 + 1.5\times IQR=72+1.5\times17=72 + 25.5 = 97.5$
Step5: Identify the outlier
The value 200 is greater than 97.5. So 200 is the outlier.
Answer:
200