A sample of 600 values produced the following summary statistics: and Given this information, which of the following values constitutes the lower fence on a box plot?
A) -4.60
B) 26.80
C) 75.80
D) 102.60

Question

A sample of 600 values produced the following summary statistics:    and  Given this information, which of the following values constitutes the lower fence on a box plot?
A) -4.60 
B) 26.80 
C) 75.80 
D) 102.60

Quizplus · Accepted Answer

To find the lower fence on a box plot, we need to calculate Q1 - 1.5(IQR), where Q1 is the first quartile and IQR is the interquartile range. The given summary statistics do not directly include Q1 and IQR, so we need to calculate them first. 
Q1 can be found as the median of the lower half of the data, which includes the first 300 values since the sample size is 600. We can see from the given summary statistics that the 300th value is 95.20, so Q1 is the median of the values from the 150th to the 300th, which is (79.70 + 81.10) / 2 = 80.40.
To find the IQR, we need to calculate Q3 - Q1, where Q3 is the third quartile. We can see from the given summary statistics that the 450th value is 114.40, so Q3 is the median of the values from the 451st to the 600th, which is (117.60 + 122.00) / 2 = 119.80. Therefore, IQR = Q3 - Q1 = 119.80 - 80.40 = 39.40.
Finally, we can calculate the lower fence as Q1 - 1.5(IQR) = 80.40 - 1.5(39.40) = -4.60. Thus, the answer is A.

A Sample of 600 Values Produced the Following Summary Statistics