Create a sample of numbers with the following four properties. There are many po

Question

Create a sample of numbers with the following four properties.

There are many possible solutions to this question, so you need to show work to demonstrate that each property is true for your sample. (4pt)

n=8

IQR= 8.5

Median= 0

All values are unique integers.

Here is what I have so far:

The directions state that all numbers used must be a unique *integer and I am having a hard time with having n=8 and there being no decimals (not an integer)... how can be IQR be 8.5 without a number being a decimal?

My data set is -5 -4 -3 -2 2 3 4.5 5
Median: (-2 + 2)/ 2 = 0 so that looked good
IQR: 4.5-(-4)= 8.5 ..... but if they can only be integers then that is incorrect. I see where j can be rounded up to a ceiling number but I am confused if my Q1 is an odd number how I would do that or how to use that formula....

Thanks,

Jax

Explanation / Answer

In case of 8 numbers, let the numbers be a, b, c, d, e, f, g, h in ascending order. Now as we are given that the median of the numbers is 0. Therefore the average of the middle 2 numbers must be 0. Now as we need unique integers. Let d = -1 and e = 1 for their average to be equal to 0. Therefore now the distribution we have is:

_ _ _ -1, 1 _ _ _

Now next we are given that the interquartile range is 8.5.

The lower quartile is computed as the 0.25*(n+1) = 0.25*9th = 2.25th value in the given data set.

The lower quartile is computed as the 0.75*(n+1) = 0.75*9th = 6.75th value in the given data set.

Now if we keep the 6th value as 4 and the 7th value as 5 then , the upper quartile value would be

Q3 = 4 + 0.75*( 5-4) = 4.75

Also if we keep the 2nd value as -4 and 3rd value as -3. Then the lower quartile would be:

Q1 = -4 + 0.25*(1) = -3.75

Therefore now the interquartile range is computed as:

IQR = Q3 - Q1 = 4.75 - (-3.75) = 8.5

Therefore the IQR condition is satisfied here.

Therefore the set of 8 numbers could be:

-5, -4, -3, -1, 1, 4, 5, 6

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.