Find the values of f₁ and f₂ of the frequency, if the mean of the following frequency distribution is 21.4 and the total frequency is 40.

Class-interval	0 - 8	8 - 16	16 - 24	24 - 32	32 - 40
Frequency	6	f1	10	f2	9

Take a = 10 and h = 8.

Class interval	Mid-point xi	fi	fi xi
0 - 8	4	6	text-align:center;mso-line-height:150%">24
8 - 16	12	f1	text-align:center;mso-line-height:150%">12 f1
16 - 24	20	10	text-align:center;mso-line-height:150%">200
24 - 32	28	f2	text-align:center;mso-line-height:150%">28 f2
auto;text-align:center;mso-line-height:150%">32 - 40	36	9	text-align:center;mso-line-height:150%">324
		25 + f1+ f2 = 40	548 + 12 f1 + 28 f2

f₁ + f₂ = 15 ……………………..(i)
∴ =
21.4 =
856 = 548 + 12f₁ + 28f₂
12f₁ + 28f₂ = 308
3f₁ + 7f₂ = 77 …………………..(ii)
(ii) - 3 × (i) ⇒
3f₁ + 7f₂ = 77
3f₁ + 3f₂ = 45
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       4f₂ = 32
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f₂ = 8 ∴ f₁ = 15 - 8 = 7