Explanation:
I could not find a way to write sigma as the capital Greek letter (and with the index indications on the top and the bottom).
so, I will simply write it like
sigma n=1 to 12 (xn)
when saying sum up all xn for n = 1 to 12.
I hope this is understandable.
m = the mean cell phone bill for the indicated period.
(a)
the whole year means all 12 months (from 1 to 12).
m = (sigma n=1 to 12 (xn))/12 =
= (83+86+78+82+95+87+90+76+88+82+83+71)/12 =
= 83.41666666... ≈ $83.42
(b)
the last 6 months are the months 7..12.
m = (sigma n=7 to 12 (xn))/6 =
= (90+76+88+82+83+71)/6 =
= 81.66666666... ≈ $81.67
(c)
from March to September are the months 3..9 (7 months).
m = (sigma n=3 to 9 (xn))/7 =
= (78+82+95+87+90+76+88)/7 =
= 85.14285714... ≈ $85.14
(d)
by looking through the list, clearly the 3 consecutive bills with the highest mean are May, June, July with $95, $87, $90.
why ? $95 and $90 are the highest bills anyway, and $87 is only $1 less than the third highest bill $88.
all other groups of 3 will have a lower sum than the mentioned 3. and therefore also their mean value will be lower (as this is just a division by the constant 3).
m = (sigma n=5 to 7 (xn))/3 =
= (95+87+90)/3 =
= 90.66666666... ≈ $90.67