Question

1. find the outlier of the data set. 40, 62, 47, 68, 12, 78, 49, 65, 49, 52, 63

Explanation:

Step1: Arrange data in ascending order

$12,40,47,49,49,52,62,63,65,68,78$

Step2: Calculate the median (Q2)

There are 11 data - points. The median is the 6th value. So, $Q2 = 52$.

Step3: Calculate the lower half and its median (Q1)

The lower half is $12,40,47,49,49$. The median of the lower half (Q1) is 47.

Step4: Calculate the upper half and its median (Q3)

The upper half is $62,63,65,68,78$. The median of the upper half (Q3) is 65.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=65 - 47 = 18$

Step6: Calculate the lower and upper bounds for non - outliers

Lower bound: $Q1-1.5\times IQR=47-1.5\times18=47 - 27=20$
Upper bound: $Q3 + 1.5\times IQR=65+1.5\times18=65 + 27=92$

Step7: Identify the outlier

The value 12 is less than 20. So, 12 is the outlier.

Answer:

12