# S1 Stats - Standard deviation

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#1

So I've worked out that the mean and standard deviation of the original 30 variables is 6.5 and and 2.11.

But I don't know how to do the second bit. Please advise?

Thanks!
0
3 years ago
#2

So I've worked out that the mean and standard deviation of the original 30 variables is 6.5 and and 2.11.

But I don't know how to do the second bit. Please advise?

Thanks!

This is what I think you have to do:

Find the mean of the 20 games - 143/20 = 7.15
Find the SD of the 20 games - √(1071/20)-(7.15/20)² = 7.309...

To find all Mean and SD of all 50 games just add them together:
Mean - 7.15 + 6.5 = 13.65
SD - 7.309 + 2.11 = 9.42 (3sf)
1
3 years ago
#3
I remember this question, this is MEI right?

firstly, calculate the new mean by adding sixma x for all the 50 games in total (i.e sigma x that is given for the additional 20 games, and the sum of the scores in the first 30 games), and dividing the total by 50, this will be the mean for the total 50 games.

then, calculate the total sigma x^2 values for the 50 games - do this by adding the given sigma x^2 for the additional 20 games to the sigma x^2 (can be calculated using the calculator), the new sum will be the sigma x^2 value for the 50 games.

Now, youve already calculated the mean, calculate the sd using

sq root of (Sxx/n-1)

1
#4
Thanks a lot for replying guys.

(Yep this is good old MEI )

So I think they wanted us to slip up and the two separate means for set 30 and set 20. This is what I did initially and it was wrong (6.5 + 7.15 = not combined mean). So then I did it the second way, which was to add the sigma of x of both sets ((195 + 143) / 50) which gave me 6.76 (this is correct - yay).

Then I squared all values in the set of 30 values, added together to get 1397. We already know the total for set of 20 values equals 1071. Added these together.

Found the sum of squares -> Formula: Sigma x^2 - n * (Sample Mean)^2
-> 2468 - 50 (6.76)^2 = 183.12. Divided this by 49 to get 3.737. Rooted it to get 1.93 which is the standard deviation.

Thank god for stat calcs.
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