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# Standard deviation question watch

1. In a random sample size of 14, the sample mean was 8.2 and the sample standard deviation was 6.2.
In another independent random sample of size 23, the sample mean was 1.9 and the sample standard deviation was 9.9.

What is the sample standard deviation of the two samples?4dp
2. Do you know how to calculate standard deviation?
Oh, it already gives you standard deviation of each sample??
3. That question makes no sense

Posted from TSR Mobile
4. (Original post by qtb4)
In a random sample size of 14, the sample mean was 8.2 and the sample standard deviation was 6.2.
In another independent random sample of size 23, the sample mean was 1.9 and the sample standard deviation was 9.9.

What is the sample standard deviation of the two samples?4dp
Ok, so this question looks difficult but when broken down it's not too bad. Let's get to it!

First off, some definitions!

n is the sample size, x̄ is the sample mean and σ is the standard deviation.

Now for some Formulas!

x̄ = ΣX / n or sample mean = sum of X values divided by sample size.

σ2 = (ΣX2/ n) - (ΣX / n)2or Variance = Mean of squares - Square of Mean

Call the two samples A and B

Sample A

n = 14
= 8.2
σ = 6.2

Sample B

n = 23
= 1.9
σ = 9.9

Let's look at Sample A first. Using the first formula we can find ΣX = 14 x 8.2, so ΣX = 114.8. Then by using the second formula and rearranging we can find that ΣX2= [ (6.2)2+8.22] x 14. Hence ΣX2 = 1479.52.

Now for Sample B. Using the same process as above, we get that ΣX = 43.7 and ΣX2 = 2337.26

Combining for both samples, n = 37, ΣX = 158.5 and ΣX2 = 3816.78

Using the second formula then we get:

σ2 = (ΣX2/ n) - (ΣX / n)2

σ2 = (3816.78/ 37) - (158.5 / 37)2

σ = 9.20898542...

or the Standard Deviation for both samples = 9.2090 to 4dp as required!

Hope this helps!

~Brandon~

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Updated: March 15, 2016
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