Question

19 below are two representations of data. a: 2,5,5,6,6,6,7,8,9 b: which statement about a and b is true? (1) median of a > median of b (2) range of a < range of b (3) upper quartile of a < upper quartile of b (4) lower quartile of a > lower quartile of b

Explanation:

Step1: Find the median of data - set A

Data - set A: 2, 5, 5, 6, 6, 6, 7, 8, 9. There are 9 data points. The median is the 5 - th value when the data is ordered. So the median of A is 6.

Step2: Find the median of data - set B from the box - plot

In a box - plot, the line inside the box represents the median. From the box - plot of B, the median is 7.

Step3: Find the range of data - set A

Range = maximum value - minimum value. For A, maximum = 9, minimum = 2, so range of A=9 - 2 = 7.

Step4: Find the range of data - set B

From the box - plot of B, the minimum value is 4 and the maximum value is 10. So range of B = 10 - 4=6.

Step5: Find the upper quartile of data - set A

There are 9 data points. The upper half of the data is 6, 7, 8, 9. The upper quartile (Q3) is the median of the upper half. So Q3 of A is $\frac{7 + 8}{2}=7.5$.

Step6: Find the upper quartile of data - set B

In a box - plot, the right - hand side of the box represents the upper quartile. For B, the upper quartile is 9.

Step7: Find the lower quartile of data - set A

The lower half of the data is 2, 5, 5, 6. The lower quartile (Q1) is the median of the lower half. So Q1 of A is $\frac{5+5}{2}=5$.

Step8: Find the lower quartile of data - set B

In a box - plot, the left - hand side of the box represents the lower quartile. For B, the lower quartile is 5.

Answer:

(3) upper quartile of A < upper quartile of B