b Which of the two methods is expected to give more accurate

(b) Which of the two methods is expected to give more accurate results for s² in general?

Solution

a) The second formula is more accurate in calculating s² as we need to take square of all values and subtract it from its mean square

b) Formula 1 would always give more accurate result

c) Consider the sample 100,103,105,109,107

mean = 104.8

s2 by formula 1 =[ (-4.8)² + (-1.8)² +(0.2)² + (4.2)² + (2.2)² ]/5 = (23.04 +3.24 + 0.04 + 17.64 + 4.84)/5 = 9.76

s2 by formula 2 = 10992.8 - (104.8)² = 10992.8 - 10983.04 = 9.76

In this case both the formula gave same result but formula 1 is more accurate