Question

If sigma 1 to 15 xi 2 = 2830 and sigma 1 to 15 xi = 170 find variance of x.

Answer 1

Given: Σx=170Σx2=2830Σx=170Σx2=2830 and increase in Σx=10Σx=10⇒Σx′=170+10=180⇒Σx′=170+10=180Increase in Σx2=900−400=500Σx2=900−400=500⇒Σx′2=2830+500=3330⇒Σx′2=2830+500=3330Correct Variance = 1n1nΣx′2−(1nΣx′2−(1nΣx′)2Σx′)2=115=115×3330−(115×3330−(115 ×180)2×180)2=222−144=222−144=78