Question

The following data shows the number of home runs hit by the top 7 home run hitters in Major League Baseball during the 2011 season.

43 41 39 39 38 37 37

The lower limit for determining outliers for a box and whisker plot is_____.

Answer 1

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
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 odd number of data points, this implies that
Median = 39.0
Lower half of our list is [37.0, 37.0, 38.0]
Since our lower half list have even number of data points, this implies that
Q1 = 37.0
Upper half of our list is [39.0, 41.0, 43.0]
Since our upper half list have even number of data points, this implies that
Q3 = 41.0
Interquartile range is equal to the distance between quartile 1(Q1) and quartile 3(Q3).
IQR = Q3 - Q2
IQR = 41.0-37.0
IQR = 4.0
1.5*IQR = 6
The lower limit for determining outliers for a box and whisker plot is = Q1 - 1.5*IQR = 37-6 = 31