Explanation:
since the new data point is exactly the mean value from the pervious data points, it will not change the mean value.
formally, the mean value is the sum of the values of the data points divided by the number of data points.
so, after the first 7 days we had
(a+b+c+d+e+f+g)/7 = 3
that means
(a+b+c+d+e+f+g) = 3×7 = 21
now, after the 8th day we have
(a+b+c+d+e+f+g+3)/8 = ((a+b+c+d+e+f+g) + 3)/8 /
= (21 + 3)/8 = 24/8 = 3
so, as expected, the mean temperature for the first 8 days did not change compared to the first 7 days and is 3°F.