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

- 20, 25, 30, 35, 40, 45

Min = ?
Max = 45

Q3 - Q1 = 10

Mean = 32.5

A. 22, 29, 34, 36, 39, 45
B. 20, 30, 35, 40, 45
C. 22, 25, 35, 35, 35, 35, 36, 44, 45
D. 22, 25, 33, 35, 37, 40, 45

Answer :

The correct answer is option D) 22,25,33,35,37,40,45.

To create a box plot, we need to find the minimum value, the maximum value, the median, and the quartiles of the data set.

  • The minimum value of the given data set is 20, which is represented by the lower whisker of the box plot.
  • The maximum value of the given data set is 45, which is represented by the upper whisker of the box plot.
  • The median of the given data set is 32.5, which is represented by the vertical line inside the box.
  • The interquartile range (IQR) of the given data set is 10, which is represented by the length of the box. The lower quartile (Q1) is 27.5 and the upper quartile (Q3) is 37.5.

Now, let's check which of the given data sets matches the information provided in the box plot:

A) 22,29,34,36,39,45: This data set does not have a minimum value of 20 or a maximum value of 45, so it cannot be represented by the given box plot.

B) 20,30,35,40,45: This data set has the correct minimum and maximum values, but it does not have a median of 32.5 or an IQR of 10, so it cannot be represented by the given box plot.

C) 22,25,35,35,35,35,36,44,45: This data set has the correct minimum and maximum values and a median of 32.5, but it does not have an IQR of 10. The Q₁ and Q₃ values are also different from the given box plot, so it cannot be represented by the given box plot.

D) 22,25,33,35,37,40,45: This data set has the correct minimum and maximum values, a median of 32.5, and an IQR of 10. The Q1 and Q3 values also match the given box plot. Therefore, this data set could be represented by the given box plot.

So, the correct answer is option D) 22,25,33,35,37,40,45.

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