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# Quick box plots check watch

1. Hi.

I came across this box plots question in a past paper. I tried it and wanted to know if anyone could check my answers to the questions to see how i faired.

The way which I have got the answer is in italics, just making sure it was correct.

The boxplots below show prices of used cars (in thousands of dollars) advertised for sale at three different car dealers.

a) Which dealer offers the cheapest car offered, and at what price?

The dealer which offers the cheapers car is Car Z and the price is \$5000.
(We know this because the outliner mark is at \$5000.)

Which dealer has the lowest median price, and how much is it?

The dealer with the lowest median price is ButIt and the price is \$12,000.
(We know this because it has the lowest difference between the lower quartile and median in all three dealers)

c) Which dealer has the smallest price range, and what is it?

The dealer with the smallest price range is Ace and that is \$10,000

[I done this by taking the smallest value away from the highest vale on all car dealers and BuyIt had the smallest number][/I]

d) Which dealers prices have the smallest IQR, and what is it?

The dealers with the smallest IQR are Ace and CarZ and that is \$3000.

[I][(I done this by working out the difference between the upper and lower quartiles on all three dealers and Ace and Car Z were both the same.)/I]

e) Which dealer generally sells the cheapest cars? Explain

The dealer which generally sells the cheapest cars is BuyIt and we know this because it has the lowest median price. Even though Car Z has the cheapest car. its median price is higher than BuyIt

Thank you

Much appreciated
2. (Original post by anon2332)
a) Which dealer offers the cheapest car offered, and at what price?

The dealer which offers the cheapers car is Car Z and the price is \$5000.
(We know this because the outliner mark is at \$5000.)
Yep.

(Original post by anon2332)
Which dealer has the lowest median price, and how much is it?

The dealer with the lowest median price is ButIt and the price is \$12,000.
(We know this because it has the lowest difference between the lower quartile and median in all three dealers)
Right answer for the wrong reason. The median is the thick black line in the middle of all of your box plots - you're just looking for which one is lowest. Nothing to do with differences.

(Original post by anon2332)
c) Which dealer has the smallest price range, and what is it?

The dealer with the smallest price range is Ace and that is \$10,000

[I done this by taking the smallest value away from the highest vale on all car dealers and BuyIt had the smallest number][/I]
Right method, wrong answer. Try again. (Why have you - in red - given two different answers?)

(Original post by anon2332)
d) Which dealers prices have the smallest IQR, and what is it?

The dealers with the smallest IQR are Ace and CarZ and that is \$3000.

[I][(I done this by working out the difference between the upper and lower quartiles on all three dealers and Ace and Car Z were both the same.)/I]
They're not the same.

(Original post by anon2332)
e) Which dealer generally sells the cheapest cars? Explain

The dealer which generally sells the cheapest cars is BuyIt and we know this because it has the lowest median price. Even though Car Z has the cheapest car. its median price is higher than BuyIt
Yes. You might want to mention that each quartile of the data (including the median) for BuyIt is less than the corresponding quartile for the other two.

For question C is the right answer Ace and \$10,000? As \$20,000 (the highest value) - \$10,000 (the lowest vlaue) = \$10,000

For question D is the right answer Ace and \$3000?

Thanks again
4. (Original post by anon2332)
For question C is the right answer Ace and \$10,000? As \$20,000 (the highest value) - \$10,000 (the lowest vlaue) = \$10,000
Nope, I already said it wasn't. There is a company with a lower range.

(Original post by anon2332)
For question D is the right answer Ace and \$3000?
No, the IQR for Ace isn't \$3000.
5. Oh right.

So question C, the dealer with the smallest price range is Car Z at \$8000? I thought you had to include the outliner when taking them away.

Question D, is Ace at \$5000?

Thank you
6. (Original post by anon2332)
Oh right.

So question C, the dealer with the smallest price range is Car Z at \$8000? I thought you had to include the outliner when taking them away.
Oh, sorry! I completely missed the outlier. (You draw your box plots differently to how I did, but that was a few years ago - I was taught to draw them including all the outliers.) Yes, the answer's Ace, at \$10,000.

(Original post by anon2332)
Question D, is Ace at \$5000?
It is. So, does it have the lowest IQR?

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