Question

The table represents the average protein intake in grams per day for people in different countries. Identify the following measures based on the given random sample of countries. Use the IQR method to determine which values are outliers

Country Angola Thailand Costa Rica Malaysia China Mexico Japan Saint Lucia Albania Germany USA Portugal Protein 34 57 71 75 82 91 92 95 96 100 114 119

Answer 1

Since we know that
The lower quartile(Q1) is the median of the lower half of the data set while upper quartile(Q3) is the median of the upper half of the data set.
Also, median for a list of even number of data point is the mean of 2 middle most values if we sort the list in increasing order while for a list of odd number it is the middle most value if the list is sorted in increasing order.
Since our list have even number of data points, this implies that
Median = 91.5
Lower half of our list is [34.0, 57.0, 71.0, 75.0, 82.0, 91.0]
Since our lower half list have even number of data points, this implies that
Q1 = 73.0
Upper half of our list is [92.0, 95.0, 96.0, 100.0, 114.0, 119.0]
Since our upper half list have even number of data points, this implies that
Q3 = 98.0
Interquartile range is equal to the distance between quartile 1(Q1) and quartile 3(Q3).
IQR = Q3 - Q2
IQR = 98.0-73.0
IQR = 25.0
Since we know that the outliers are those points in the data set which are either less than 1.5 times the IQR from Quartile 1 or more than 1.5 times the IQR from Quartile 3
Therefore only this point is an outlier
34.0 (Angola)
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