The summary statistics for the yield of a ceramic substrate

The summary statistics for the yield of a ceramic substrate is shown below. Use the process involved in building a boxplot to determine if there are any outliers. Show your work, and write yes or no in the box.

Mean: 90.517

Median: 90.900

Standard Deviation: 2.965

Min: 86.100

Max: 95.100

Q1: 87.525

Q3: 93.000

Solution

in a box plot we construct inner fences to the left and right of the box at a distance of 1.5 times the INTERQUARTILE RANGE from the median.

outer fences are constructed at a distance of 3 times the INTERQUARTILE RANGE from the median.

INTERQUARTILE RANGE=Q3-Q1

observations that lie beyond the outer fences are called outliers

observations that lie within inner and outer fences are called suspected outliers.

now the interquartile range is Q3-Q1=93-87.525=5.475

so the inner fences are at points

median-1.5*5.475=90.9-1.5*5.475=82.6875

and at median+1.5*5.475=90.9+1.5*5.475=99.1125

the outer fences are at points

median-3*5.475=90.9-16.425=74.475

and at median+3*5.475=90.9+16.425=107.325

so any value lying above 107.325 or below 74.475 will be considered as an outlier

any value lying above 99.1125 but below 107.325   or below 82.6875 but above 74.475 will be considered as suspected outlier.

but here the max value is 95.1 which lies below 99.1125

and the min value is 86.10 which lies above 82.6875

so all the values lie below 99.1125 and above 82.6875

so there are no outliers or suspected outliers.