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Question: The median price of different books in a bookstall is $35.The difference between twice the minimum price and half the maximum price in the bookstall gives the median price, which is also equal to the midrange. The IQR of the prices is $5. The price of the book corresponding to 25th percentile is $32. Identify five - number summary .


A ) 28, 32, 35, 37, 42
B ) 28, 42, 32, 35, 37
C ) 28, 37, 42
D ) 12, 24, 35, 40, 56

Steps to derive

1 Let the minimum price of the book be x and maximum price of the book be y.

2 2x - y2 = 35
4x - y = 70 ... (1)
 [Given median = 35.]

3 2x - y2 = x+y2
 [Given median = midrange.]

4 4x - y = x + y
3x - 2y = 0 ... (2)

5 Solve (1) and (2)
8x - 2y = 140
3x - 2y = 0
____________
5x = 140
x = 1405 = 28

6 If x = 28 then y = 42
 [From step 2, 3x = 2y.]

7 So, the minimum price in the book stall is 28 and maximum price in the book stall is 42.

8 The price of the book corresponding to 25th percentile is $32.

9 So, Q1 = 32
 [Q1 is the 25th percentile.]

10 Q3 - Q1 = 5
Q3 - 32 = 5, Q3 = 37
 [Given IQR = 5.]

11 The five - number summary is 28, 32, 35, 37, 42.



Hence the right answer is Option A

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