Question

I bought two packets of apples, 25 in each packet. The mean and standard deviation of
weights of apples in the first packet are 235 and 3; and the mean and standard deviation for
the second packet are 237.5 and 4. Write down the mean and standard deviation formulae for
all the fifty apples and compute them.

Answer 1

combined mean =  ( μ₁ n₁ + μ₂ n₂) / (n₁ + n₂)
        = ( 25 * 235 + 25 * 237.5 ) / 50 = 236.25

combined standard deviation = [ (σ₁² n₁ + σ₂² * n₂) / (n₁+n₂) ]¹/²
       = [ (3² * 25 + 4² * 25) / 50 ]¹/²  = √12.5