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the mean of 5 apple is $12$, the range of the biggest and the lowest is $6$. If every apple is subtracted by $a$ then the sum is divided by $b$, the new mean is $2$ and the range of the biggest and the lowest is $3$. Find $a$ and $b$.

Carlos Eugenio Thompson Pinzón
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Jeniffer
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  • "the mean of 5 apple is 12" – user85798 Oct 30 '13 at 11:16
  • @Oliver yes it is xD, but I am confused about what's a and b :(. – Jeniffer Oct 30 '13 at 11:23
  • @Jeniffer What he means is that "the mean of $5$ apple is $12$" doesn't mean anything. Are the "apples" just pieces of data? For instance measurements of the sizes of the applies or something? So the mean of those $5$ measurements is $12$? – Jack M Oct 30 '13 at 11:27
  • In any case, $a$ and $b$ are unknowns, that's the point of the problem. You're supposed to figure out what they are from the information you're given. – Jack M Oct 30 '13 at 11:29
  • I don't get it. – Dan Shved Oct 30 '13 at 11:39
  • Let me guess what you mean. You have five values (v.g the weight in ounces of five apples). Those five values have a mean of $12$ and a distribution of $\pm6$. Right? What happen with mean and distribution if each of those values are substracted by the same amount $a$? What happen with mean and distribution if they are divided by the same amount $b$? – Carlos Eugenio Thompson Pinzón Oct 30 '13 at 11:40
  • I have no idea how to subtract a number from an apple. – Dan Shved Oct 30 '13 at 11:40

1 Answers1

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ok I am going to answer this question assuming that it is measuring a piece of information about the apple that has a mean of 12. It could be the number of apples in a batch, it could be the diameter, or radius but the answer will still be the same

So we have a data set: $\{v,w,x,y,z\}$

$v$ is the mesaurement of the first apple, $w$ is the measurement of the second apple and so on.

we know that the following

$\frac{v+w+x+y+z}{5}=12$ and $z-v=6$

when we do the changes, our new data set is: $\{\frac{v-a}{b},\frac{w-a}{b},\frac{x-a}{b},\frac{y-a}{b},\frac{z-a}{b}\}$

And we know that from that data set we have the following (I have simplified the equations):

$\frac{v+w+x+y+z-5a}{5b}=2$ and $\frac{z-v}{b}=3$

In the second one, we know that $z-v=6$ from the previous equation so we can substitute that in and find that $b=2$

We can also factor out the original mean from the third equation and get the following:

$\frac{1}{b}\times(\frac{v+w+x+y+z}{5}-\frac{5a}{5})=2$

We can substitute that mean inside with $12$ and $b$ with $2$

$\frac{1}{2}\times(12-a)=2$

$6-\frac{a}{2}=2$

$-\frac{a}{2}=-4$

$a=8$

Therefore we have found that $a, b=8,2$

If you need help understanding this just ask

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