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Question: The upper quartile of a data set is the 9th data value of the set. How many data values does the entire data set have?


A ) 10
B ) 12
C ) 11
D ) 8

Steps to derive

1 The three quartiles divide an entire data set into 4 equal parts.

2 Let x be the number of data values in each part.

3 The position of the upper quartile will be 3x + 3
 [Three equal parts + one lower quartile + one middle quartile + 1.]

 [Given the position of the upper quartile of the set is 9.]
4 9 = 3x + 3

 [Subtract 3 from each side.]
5 6 = 3x

 [Divide both sides by 3.]
6 x = 63 = 2

7 So, each part contains 2 data values.

8 The total number of data values = 4x + 3
= 4 × 2 + 3
 [Four equal parts + three quartiles.]

 [Simplify.]
9 = 11

10 So, there are 11 data values in the entire data set.



Hence the right answer is Option C

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