Question

If mean of following data is 21.5, then find K.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	6	4	3	K	2

Answer 1

∵ Arithmetic mean = \(\frac { { \Sigma f }_{ i }{ x }_{ i } }{ { \Sigma f }_{ i } }\)

21.5 = \(\frac { 255+35K }{ 15+K }\)

⇒ 322.5 + 21.5 = 255 + 35K

⇒ 322.5 – 255 = 35K – 21.5K

⇒ 13.5K = 67.5

K = \(\frac { 67.5 }{ 13.5 }\) = 5

∴ K = 5