Question

1. find the outlier of the data set. 44, 67, 52, 72, 82, 55, 70, 200, 55, 57, 68

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