Posted by Lenny on .
150 students sat exams. The following elements were calculated
ΣFX = 10200
Σ(xμ)F = 196348
Determine the number of students whose marks were within 2 standard deviations of the mean score

Math 
David Q,
Are you sure that second formula isn't Ó(xì)²F? Unless it is, I can't see a way of calculating a standard deviation from the statistics supplied.
On the assumption that the second statistic is Ó(xì)²F, the variance ought to be (1/150) times this figure, which is 196348/150 = 1309, so the standard deviation would be 36.2, with a mean of 10200/150=204. So any student with a score of between 204(2x36.2) and 204+(2x36.2) would be within two standard deviations of the mean.
Having said all that, you asked for the actual number of students within that range  and it seems to me that you don't actually need either of the statistics given to answer that question. If the scores are Normally distributed, then 4.6% of the distribution ought to lie outside two standard deviations (i.e. either in the lower or the upper tail). Out of 150 students that's 7 students  so 143 ought to lie inside plus or minus two standard deviations. (I can't see any way to tell *exactly* how many students lie within that interval, even from the statistics supplied.) 
Math 
David Q,
(Sorry  the symbols Ó and ì ought to be a sigma sign and a mu respectively. You evidently can't just copy them from another posting  it doesn't work.)