S1 question help?

mean = sum of x/n

so sum of x = n x mean
14x 31.2 =436.8

adding the new student means that sum of x is now 436.8 + 42 = 478.8

therefore, new mean = sum of x/n
478.8/15 = 31.92



for the standard deviation, for the original class:

(standard deviation is the square root of variance)
σ² = Σx²/n – mean²

7.4² = Σx²/14 – 31.2²

rearrange that to get Σx² = 14394.8

then, adding in the new student:

14394.8 + 42² = 16158.8 (this is the new Σx²)

therefore, the new standard deviation is the square root of:

16158.8/15 – 31.92²