gcse statistics - the mean & standard deviation?

1) mean=19.6 is correct
standard deviation =58.8 is wrong, standard deviation is usually a small value

Sum x^2=3934
Sum x=196

Apply the formula for standard deviation sqrt 3934/10 - (196 / 10)^2 = 3.039736...
approximately = 3.04 (2d.p)

and then the girls had to sit a mental maths test which takes 5 mins

That means 1 more girl is now in the sample so n=11, sum x=201, sum x^2=3959

So mean=sum x/n = 18.272727... approximately=18.27 (2d.p)

Standard deviation= sqrt 3959 /11 - (201/11)^2=5.10064 approximately = 5.1 (1d.p)

2) 21 archer took part in a competition and each got a score out of 600. the sum of their scores is 9669. the sum of the squares of their scores is 4473290.

Mean=460.4 is correct
Standard deviation= 31.9 is also correct as well.

Difference of 353-348=5
Sum x=9674 and Sum x^2 is a little bit tricky to find.

Ok you know 348^2=121104
Sum x^2=4473290-121104=4352186
4352186+353^2= 4476795

Now you know Sum x=9674 and Sum x^2=4476795 and n=21

mean= 460.6666 approximately=460.7 (1d.p) correct
standard deviation= 31.0956... approximately = 31.096 (3d.p)

Hope it helps. I skip some steps of calculation, you just need to apply them in the formula and you should be able to get it. Good luck and practice more.

Additional Details
btw part 2 of Q1 asks for the mean and standard deviation of the total times taken for both tests

1st test: Sum x=196, Sum x^2=3934, n=10
2nd test: Sum x=201, Sum x^2=3959, n=11

Total time means adding these values together

Total: Sum x=397, Sum x^2=7893, n=21
Apply the formula, you should get
Mean=18.9047... approximately = 18.9(1d.p)
Standard deviation=4.29733.. approximately = 4.3(2d.p)

Hope it helps and good luck.

The extra decimal places you take advantage of for the calculation the further precise your answer will be. so that you'll do an same sum utilising the mean as 2 then repeat utilising the mean as 2.4 and repeat utilising 2.38 and repeat utilising 2.384 and so on and each and anytime you would get an prolonged calculation yet a extra precise effect. do not forget once you sq. those numbers you receives 6 decimal places for the sq. of a three decimal form even if the accuracy will in common words be as precise because the starting up documents grow to be eg probable to at least a million decimal position if the raw documents grow to be in common words measured to at least a million decimal position.