Question

The five number summary of a dataset was found to be:

46, 49, 55, 67, 69

An observation is considered an outlier if it is below:

An observation is considered an outlier if it is above:

Answer 1

The given data set-

46,49,55,67,69

The values are already in Ascending Order.

Number of observations= 5

The median is 55( Median means the middle-most value of the data set)

The lower/first quartile of the data set, Q₁ = (46 + 49)/2 = 47.5

( Since, lower/first quartile is the middle point of the 2 values below 55)

The upper/third quartile, Q₃ = (67 + 69)/2 = 68

( Since, upper/third quartile is the middle point of the 2 values above 55)

The Interquartile Range (IQR) = Upper Quartile - Lower Quartile = 68 - 47.5 = 20.5

Now, Outlier is an observation that lies outside the overall distribution

By the IQR rule,

We multiply 1.5 to the IQR and subtract that value from Lower Quartile to check for low outliers

Thus, Q₁ - (1.5 x IQR) = 16.75

An observation is considered an outlier if it is below: 16.75

We multiply 1.5 to the IQR and add  the  value to the Upper Quartile to check for high outliers.

Thus, Q₃ + ( 1.5 x IQR ) = 98.75

An observation is considered an outlier if it is above: 98.75

In this case, there are no outliers in the data set.