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

Quizplus · Accepted Answer

To calculate the upper fence on a box plot, we use the formula:
Upper fence = Q3 + 1.5*IQR
where Q3 is the third quartile and IQR is the interquartile range.

From the given summary statistics, we can see that the third quartile (Q3) is 75.80 and the interquartile range (IQR) is the difference between the third quartile and the first quartile (Q1). Unfortunately, we don't have Q1 in the summary statistics. However, we do have the minimum value (11eab386_b97a_707e_aec0_13dceddb5180_TB4962_11), which is equivalent to Q0 (the zeroth quartile, or the minimum value).

So, we can estimate Q1 as follows:
Q1 = Q0 + (IQR/4)
where IQR = Q3 - Q1
Thus, we can calculate:
IQR = Q3 - Q1
IQR/4 = (11eab386_b97a_707e_aec0_13dceddb5180_TB4962_11 + Q1)/2
Substituting Q3 = 75.80 and solving, we get:
Q1 = 39.10

Now, we can calculate the upper fence:
Upper fence = Q3 + 1.5*IQR
Upper fence = 75.80 + 1.5*(75.80 - 39.10)
Upper fence = 102.60

Therefore, the correct answer is D) 102.60

A Sample of 600 Values Produced the Following Summary Statistics