Calculating pooled standard deviation for more than two groups of unequal sample size

#1
Hi all,

I struggle with calculating the pooled standard deviation for more than two groups of unequal sample size.

After searching the internet and trying to plug in my numbers to various formula's found online, I am unable to get the answer that is proposed by the answer model. Probably this is due to mistakes in how I calculated it instead of the formula's of course.

I have the following numbers

Group 1 - 448 respondents - Mean 70,42 - Standard deviation 18,269
Group 2 - 91 respondents - Mean 71,21 - Standard deviation 18,830
Group 3 - 51 respondents - Mean 80,51 - Standard deviation 14,577

I calculated the overall mean by doing the following -- which is correct according to the answer model:
(448 * 70,42) + (91 * 71,21) + (51 * 80,51) / (448 + 91 + 51) = 71,41 (rounded)

Furthermore the overall standard deviation, according to the answer model is 18,260.

Can someone explain how this 18,260 is calculated and if possible, in addition to providing a formula, also simply plug my numbers into the formula so I can exactly see how I should do it? Sometimes I even make mistakes in the plugging-in part, so that would really help.