Question

Which data set could be represented by the box plot shown below?

Answer 1

Answer:

  (D)

Step-by-step explanation:

The box plot is a visual representation of the 5-number summary of the data. It shows the extremes, the quartiles and the median.

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Each data set has 11 elements, sorted into increasing order.

extremes

The first and last elements of the data set correspond to the ends of the whiskers, so you are looking for a set that ranges from 3 to 18. (This eliminates choice B.)

median

The median will be the middle element, the 6th from either end. The vertical line in the box identifies its value as 10. (This eliminates choice A.)

quartiles

The first quartile is the middle element of the bottom half of the data set (what remains after the median and above elements are removed). There are 5 elements in the bottom half, so the first quartile is the 3rd one. It is signified by the left end of the box in the box plot. Its value is 7. (This eliminates choice C.)

Similarly, the third quartile is the 3rd element from the right end of the data set. The value 13 in choice D matches the right end of the box in the box plot.

The box plot represents the data set in Choice D.