Lucas recorded his lunch expenditure each day for one week in the table below.Find the standard deviation. Round to the nearest thousandth. (3 points)Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Expenditure $4.85 $5.10 $5.50 $4.75 $4.50 $5.00 $6.00

Question

Lucas recorded his lunch expenditure each day for one week in the table below.Find the standard deviation. Round to the nearest thousandth. (3 points)Sunday	Monday	Tuesday 	Wednesday 	Thursday 	Friday 	Saturday 
Expenditure	 $4.85	$5.10 	$5.50 	$4.75 	$4.50 	$5.00 	$6.00

anonymous · Answer

any help?

e.mccormick · Answer

Know your standard deviation formula?

anonymous · Answer

$$\Large
\mu = \frac{1}{n}\sum_{i=1}^n x_i
$$$$\Large
\sigma^2 = \frac{1}{n}\sum_{i=1}^n (x_i-\mu)^2
$$

anonymous · Answer

First find the mean $\mu$.
Then find the standard deviation $\sigma$

e.mccormick · Answer

@wio Isn't that the population one, rather than sample?  I would think with a set of lunches it would be sample SD.

e.mccormick · Answer

If it was all the lunces Lucas ever ate, I would think $\frac{1}{n}$, but for a single week $\frac{1}{n-1}$

anonymous · Answer

What is the issue?  I don't quite get your protest.

e.mccormick · Answer

There are two different standard deviation formula.  One is used when you are working with values from the entire population.  The other is used when you only have a sample.  The sample one has a greater margin of error.

anonymous · Answer

what is your sample one?

e.mccormick · Answer

The only difference is in the 1/n vs 1/(n-1) in the SD formula.

anonymous · Answer

I've never heard of that formula.

anonymous · Answer

I have to use the equation  o=squareroot of E(x-xline)^2/n

anonymous · Answer

i am thinking that it is the 1/n equation maybe

e.mccormick · Answer

Yes, that is the 1/n form. @wio Ref for ya: http://www.mathsisfun.com/data/standard-deviation-formulas.html

e.mccormick · Answer

@hollie01 The $\bar{x}$ means to take the mean (average) and use that there.

anonymous · Answer

ok what does the n mean
I found the top part but dont know how to finish it

e.mccormick · Answer

n is the number of things.

anonymous · Answer

so i got .299 for the top part so i would then divide that by 7?

e.mccormick · Answer

yes

anonymous · Answer

is .299 correct for the top?

e.mccormick · Answer

gimmi a min.  hehe

e.mccormick · Answer

OK... for the sum of the squares of the difference, I got 1.525...  Hmmm....

e.mccormick · Answer

Lets work though this together and see where yours and mine are different.  I sum the 5 values and get 35.7, then divinde them by 7 and have a mean of 5.1.  With me there?

anonymous · Answer

dont you then have to divide by the mean which is 5.1

e.mccormick · Answer

Where are you dividing by the mean?

e.mccormick · Answer

Once you have the mean, you use it in the second sum.

anonymous · Answer

when i added the 7 values together, i got 1.525 n then divided that by the mean which is 5.1 to get .299 and then took that divided by 7 to get .043 because there are 7 values.

e.mccormick · Answer

There is nothing in there that says to divide by the mean.  What you divide by is the number and that is the end.

anonymous · Answer

so you take .299 divided by 7?

e.mccormick · Answer

No.  1.525/7 = the SD.

anonymous · Answer

ok so if the sample size increases but the sum of the squared differences stays the same, what will be the effect on the standard deviation and what would it mean in real life?

e.mccormick · Answer

You are dividing by the mean when you do not need to.  Look bacl at the second equation wio wrote.  The $\mu$ there is the same as $\bar{x}$

anonymous · Answer

i got .213 for th sd

anonymous · Answer

rounding to the hundreths place

e.mccormick · Answer

I got .218, but I was not rounding before the answer, so it is porbably just a rounding difference.

e.mccormick · Answer

Yah, I did the earlier rounding and it got me that.

anonymous · Answer

ok so what about my other question

e.mccormick · Answer

Well, the 1/n is the error adjustment.  As n gets bigger, what happens to the value of the fraction?  As in 1/7th vs 1/23rd.

anonymous · Answer

it would increase

e.mccormick · Answer

Think a second.  Which is bigger?  1/7th or 1/23rd?

anonymous · Answer

1/7

e.mccormick · Answer

So as 1/n changes because n is increasing, then the fractoion is decreasing.  Now, if the fraction is the adjustment for error....

anonymous · Answer

so the standard deviation would decrease and what would that then mean in real life

e.mccormick · Answer

Yes, and you would have a more accurate number.  So when you poll 7 people on something, you get an answer but it does not mean much.  On the other hand, if you pole 700 people, you begin to get a more accurate representation of the people.  Pole 70,000 and you pretty much know what the country is thinking with very little error.

e.mccormick · Answer

Or in this example, find out what 10,000 people paid for lunch for a week and you have the average price of lunch for the entire nation without much error.

e.mccormick · Answer

I hope that helps you understand why the 1/n matters.

anonymous · Answer

i have another question if you are willing to help

e.mccormick · Answer

Sure.

anonymous · Answer

Suppose you are researching the eating habits of people your age. What sampling method could you use to find the percent of students in your grade who eat five servings of fruit and vegs. each day. What is an example of a survey question the does not have bias?

anonymous · Answer

I was thinking random but not sure?

e.mccormick · Answer

You would want a random sample.  That is always true when you are looking for people of a certain group.  However, how you get the random sample changes things.  For example, if you do a rangom sample of people going to a school in a good part of town, it will be biased based on that part of town.

e.mccormick · Answer

Another problem would be if you were doing this for your school and the only people you talked to were your friends.  That is what the random sample is there to fix.