Question

assume this is a positive ordered set of data. which statistics show values that would most likely describe the following set of data? x, 9, 11, 13, y, 20
range = 17
median = 10
mean = 12
range = 23
interquartile range = 7
interquartile range = 12
describe the data
do not describe the data

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum. The maximum value in the set could be 20. If Range = 17, then Minimum = 20 - 17=3, so X could be 3. If Range = 23, then Minimum=20 - 23=- 3, but data is positive - ordered, so Range = 23 is not valid.

Step2: Recall median formula

For a set of 6 data points (X, 9, 11, 13, Y, 20), the median is the average of the 3rd and 4th - ordered values. Median=$\frac{11 + 13}{2}=12
eq10$, so Median = 10 is not valid.

Step3: Recall mean formula

Mean=$\frac{X + 9+11 + 13+Y + 20}{6}=12$. Then $X + Y+53 = 72$, so $X + Y=19$. Since data is ordered and positive, this is possible.

Step4: Recall inter - quartile range (IQR) concept

First, find the median of the lower half and upper half. For a set of 6 data points, the lower half is {X, 9, 11} and upper half is {13, Y, 20}. If X is small enough, the median of the lower half is 9 and median of the upper half is Y. IQR = Y - 9. If IQR = 7, then Y = 16 and X = 3. If IQR = 12, then Y = 21 which is not possible as 20 is the largest value given.

Answer:

Describe the data: Range = 17, Mean = 12, Interquartile range = 7
Do not describe the data: Median = 10, Range = 23, Interquartile range = 12