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jennimkim
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Guide 5 (Word Problems)- pg. 105, problems 1 & 13

by jennimkim Tue Mar 10, 2015 2:31 am

Hello,
Could you please work through problems 1 and 13?

1. The average of 11 numbers is 10. When one number is eliminated, the average of the remaining numbers is 9.3. What is the eliminated number?
*How do you get 9.3?

2. N is a normally distributed set with a mean of 10. If approximately 2% of the observations in N are -10 or smaller, what fraction of the observations are between 0 and 5?

Thank you!
n00bpron00bpron00b
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Re: Guide 5 (Word Problems)- pg. 105, problems 1 & 13

by n00bpron00bpron00b Tue Mar 10, 2015 1:57 pm

I can help you out with the 1st question.

1. The average of 11 numbers is 10. When one number is eliminated, the average of the remaining numbers is 9.3. What is the eliminated number?
*How do you get 9.3?


9.3 is the average after eliminating one value from a set of 11 numbers. (Consider this as given information which will aid us in finding the eliminated number. We need not worry how 9.3 was achieved)

Average Formula -
Avg = (Sum)/total

Average of 11 numbers is 10 (given)
10 = (Sum)/11
Sum = 110

Total Sum of 11 numbers is 110

Now, the question states that when one number is eliminated the average becomes 9.3

Let the eliminated number be say "x"

Avg = (Sum)/total
9.3 = (110-x)/10
93 = 110-x
x = 17

17 is the eliminated number

Cross check -

For 10 numbers

Sum of 10 numbers = 93
Avg = (sum)/total
Avg = 93/10 = 9.3 (matches the condition given in problem stm.)

For 11 numbers

11th number is 17

Sum of 11 numbers = 93 + 11th number (i.e 17) = 93 + 17 = 110
Avg = Sum/total
Avg = 110/11
Avg = 10 (matches the condition given in problem stm.)
tommywallach
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Re: Guide 5 (Word Problems)- pg. 105, problems 1 & 13

by tommywallach Thu Mar 12, 2015 8:04 pm

Hey Jenni!

1.

Nice to see you here. (In the future, please only do one question per thread, just because it keeps things clearer!).

Noob's explanation is totally right. You can also look at this using weighted averages. It's more conceptual, which makes it harder, but it's also much faster:

We removed a number, and it caused 10 numbers to go down by .7 each (on average). That means we lost a number that had a value 7 greater than our previous average (10 * .7 = 7). So the number had to be 17.

13.

In a normal distribution, 2% of the set is between 2 and 3 standard deviations below the mean. So if 2% of the data is less than -10, than -10 is the boundary for two standard deviations below the mean. That means each standard deviation is 5.

The range from 0-5 would be the ONE standard deviation immediately to the right of the average, which always makes up 1/3rd of the data. (This is described on page 101, where it says "Roughly 2/3 of the sample will fall within 1 SD of the mean. That means that roughly 1/3 of the sample falls within 1 standard deviation below the mean and roughly 1/3 of the sample falls within 1 standard deviation above the mean.").

Hope that all makes sense!

-t