A sample of 50 values produced the following summary statistics: and Based on this information, what are the left and right ends, respectively, of the box plot using whiskers?
A) 5.3 and 32.0
B) 10 and 14.6
C) 10 and 16.7
D) 14.6 and 16.7

Question

A sample of 50 values produced the following summary statistics:    and  Based on this information, what are the left and right ends, respectively, of the box plot using whiskers?
A) 5.3 and 32.0 
B) 10 and 14.6 
C) 10 and 16.7 
D) 14.6 and 16.7

Quizplus · Accepted Answer

To find the left and right ends of the box plot, we need to use the interquartile range (IQR) and the upper and lower fence calculations. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1): Q3-Q1 = 16.7 - 10 = 6.7.

The lower fence is the value of Q1 minus 1.5 times the IQR: 10 - 1.5(6.7) = 0.95. However, since the lowest value in the sample is higher than this, the left whisker will extend to the lowest value, which is 5.3.

The upper fence is the value of Q3 plus 1.5 times the IQR: 16.7 + 1.5(6.7) = 27.85. Again, since the highest value in the sample is even higher than this, the right whisker will extend to the highest value, which is 32.0.

Therefore, the left and right ends of the box plot using whiskers are 5.3 and 32.0, respectively, which corresponds to choice C.

A Sample of 50 Values Produced the Following Summary Statistics