#### chiba

10+ Year Member
I searched this forum regarding these questions but was unable to find them.

#37: The numbers (1,2,3,6) have an average (arithmetic mean) of 3 and a variance of 3.5. What is the average (arithmetic mean) and variance of the set of numbers (3,6,9,18)

How do you find variance?
Isn't it
S^2= sum (x-average)^2 / n-1 ?
I don't know how to get 31.5!

#38. Jill has 6 different books. in how many ways can Jill select 2 different books?
answer is 30 but I got 15.
let n=6
let r=2
n!/r!(n-r)! =15...
I dont get it PLEASE HELP! my exam is next week and I still don't know how to solve these #### vvvv

10+ Year Member
first problem: you used a correct equation.
second: there will be 6 ways to choose the first book, and 5 ways to choose the second (because you already chose 1) and product rule ....6x5=30

hope it help

#### jay47

##### Think Positively!
10+ Year Member
5+ Year Member
Just a general rule of thumb, when doing the math probability questions, try to think about them logically. Don't just jump in and try to plug in equations.

For example, do what the guy above me did: she can choose 6 books at first, but because she already chose another, she could only choose 5 the second "event". It's really easy if you just think about it that way.

#### eatkabab

10+ Year Member
the first one you got it correct. you've got the right equation, just takes a little working. you should be able to do it in your head in about a minute.

average is 9, subtract from each, you get 6,3,0,9, square each and add, you get 126, divide by n-1. but I do see one problem, the answer should be 9,42 not 9,31.5. to get 31.5, you divide by n, or, 4. to get the standard variance, you divide by n-1, which would be 3. 126/3 is 42...

as for the second problem, this is the difference between a permutation and a combination.

for a permutation, the order you choose your items doesn't matter. this is the case with the question you're asking. it does not matter how you select the two books, you just select them. the eqtn for this is n!/(n-r). it would be 6!/4! which is 6X5, or, 30.

a combination is a little more tricky and difficult to spot. this is when the order you choose your items in DOES matter. for example:

you have 3 red balloons, 4 yellow, and 5 blue, how many ways can you choose 3 balloons?

so the eqtn for a combination is what you have, n!/[(r!)(n-r)!]. that extra r! in the denominator makes all the difference. so the answer to this question would be 12!/[3!(9!)], or, 220... without that extra r!, you'd get 1320 which is the wrong answer.

GOOOOOD LUCK!!!

oh and if you can help me out, I'm looking for what the DAT is talking about when it asks for Descriptive and Experimental embryology. particularly implanting certain cells into a chicken or rat embryo and having the animal grow weird stuff... where do I learn this **** from?!

by the way, my exam is on the 30th... :-(

#### chiba

10+ Year Member
Thank you guys!
But for the first question, does this mean that the ADA answer was incorrect?

eatkabab, I just looked at drosophila bicoid stuff. I have embryology textbook which i used in 3rd year but don't have time to go over it so kinda gave up on that subject...

#### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
You actually don't need an equation for #1 to get it right.

You are multiplying each number in the set by 3. Since the mean is a linear function, you multiply the original mean by 3 and you will get the new mean. And sure enough, 3x3 = 9.

Since variance is a quadratic function, you just multiply the original variance by 3^2 = 9. And sure enough, 3.5x9 = 31.5.

#### chiba

10+ Year Member
Thank you Streetwolf! makes sense.. #### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
Be careful with standard deviation though because that is also linear (square root of variance). So the standard deviation would be 3x that of the original standard deviation.

#### FutureDentalStudent11

the first one you got it correct. you've got the right equation, just takes a little working. you should be able to do it in your head in about a minute.

average is 9, subtract from each, you get 6,3,0,9, square each and add, you get 126, divide by n-1. but I do see one problem, the answer should be 9,42 not 9,31.5. to get 31.5, you divide by n, or, 4. to get the standard variance, you divide by n-1, which would be 3. 126/3 is 42...

as for the second problem, this is the difference between a permutation and a combination.

for a permutation, the order you choose your items doesn't matter. this is the case with the question you're asking. it does not matter how you select the two books, you just select them. the eqtn for this is n!/(n-r). it would be 6!/4! which is 6X5, or, 30.

a combination is a little more tricky and difficult to spot. this is when the order you choose your items in DOES matter. for example:

you have 3 red balloons, 4 yellow, and 5 blue, how many ways can you choose 3 balloons?

so the eqtn for a combination is what you have, n!/[(r!)(n-r)!]. that extra r! in the denominator makes all the difference. so the answer to this question would be 12!/[3!(9!)], or, 220... without that extra r!, you'd get 1320 which is the wrong answer.

GOOOOOD LUCK!!!

oh and if you can help me out, I'm looking for what the DAT is talking about when it asks for Descriptive and Experimental embryology. particularly implanting certain cells into a chicken or rat embryo and having the animal grow weird stuff... where do I learn this **** from?!

by the way, my exam is on the 30th... :-(
you mixed up permutation and combination... in a combination order doesn't matter whereas in a permutation order does matter (but your formulas are correct)

#### Halimaw

I know this is frustrating, because there shouldn't be inconsistencies in math, but there are two equations used for variance:
S^2= sum (x-average)^2 / n-1 This is the first.
S^2= sum (x-average)^2 / n This is the second.
DAT tests use the second. The same goes for the standard deviation equation. Use "n" in the denominator, not "n-1"
126/4=31.5