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S1 Solomon Paper help

I'm stuck on a S1 question and I've looked at the mark scheme and I still don't understand. Any help appreciated. An adult evening class has 14 students. The ages of these students have a mean of 31.2 years and a standard deviation of 7.4 years.
A new student who is exactly 42 years old joins the class. Calculate the mean and standard deviation of the 15 students now in the group. I understand how to get the new mean, but not the standard deviation. The mark scheme says that you need to get the new sum of x^2; by using [14(7.4^2+31.2^2)]+42^2. I understand the need for the sum of x^2 in order to get the standard deviation, but not why it is calculated like this, could someone please explain.
(edited 8 years ago)
Original post by tas1998
An adult evening class has 14 students.

The ages of these students have a mean of 31.2 years and a standard deviation of 7.4 years.
A new student who is exactly 42 years old joins the class. Calculate the mean and standard deviation of the 15 students now in the group.

[14(7.4^2+31.2^2)]+42^2.


The first step would be the (7.4^2) + (31.2^2). What do each of the numbers represent? Hence what does their sum represent?
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tas1998
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the square of the s.d., or the variance, and the mean squared. The bit i dont understand is why the variance is involved when we are only working out sum of x^2 at this point. Is it just a formula I haven't seen before?
Original post by tas1998
the square of the s.d., or the variance, and the mean squared. The bit i dont understand is why the variance is involved when we are only working out sum of x^2 at this point. Is it just a formula I haven't seen before?


Yes, both right :smile:

They're using variance because the sum of x^2 has something to do with E(X^2).

So that bit is (I'm not sure if this notation is seen in S1, if not, sorry!) using Var(X) = E(X^2) - (E(X))^2, E(X^2) = Var(X) + (E(X))^2.

[14(7.4^2+31.2^2)]+42^2]

So that explains the thing in the round brackets, but why are they multiplying that by 14? (Hint: n is 14). You'll probably have seen a formula for finding just E(X^2).
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tas1998
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Original post by SeanFM
Yes, both right :smile:

They're using variance because the sum of x^2 has something to do with E(X^2).

So that bit is (I'm not sure if this notation is seen in S1, if not, sorry!) using Var(X) = E(X^2) - (E(X))^2, E(X^2) = Var(X) + (E(X))^2.

[14(7.4^2+31.2^2)]+42^2]

So that explains the thing in the round brackets, but why are they multiplying that by 14? (Hint: n is 14). You'll probably have seen a formula for finding just E(X^2).


Ok, thanks a lot. Yes, I do vaguely recognise that notation but I have just restarted s1 revision and getting a bit confused. I understand now, thankyou.

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