Question

Mean of 100 items is 60 and their standard deviation is 20. then the sum of squares of all the items is

Answer 1

Mean of 100 items (x̄) = 48

Standard deviation (σ) = 10

here we have to answer for two questions that is sum of all items (Σ x) and sum of squares all items (Σ x²).

x̄ = (Σ x/n)

48 = (Σ x/100)

Σ x = 100 x 48

     = 4800

Sum of all items = 4800

To find sum of squares of all items, we have to find variance (σ²).

σ² = (Σ x²/n) - (Σ x/n)²

(10)² =  (Σ x²/100) - (4800/100)²

(10)² =  (Σ x²/100) - (48)²

100 = (Σ x²/100) - 2304

100 + 2304 = (Σ x²/100)

2404 = Σ x²/100

Σ x² = 2404 (100)

Σ x² = 240400

Sum of squares of all items = 240400