KnowledgeBoat Logo

Mathematics

The mean of the following frequency distribution is 50, but the frequencies f1 and f2 in class 20-40 and 60-80 respectively are not known. Find these frequencies.

ClassFrequencies
0-2017
20-40f1
40-6032
60-80f2
80-10019

Given that the sum of frequencies is 120.

Statistics

2 Likes

Answer

ClassFrequencies (f)Class marks (x)fx
0-201710170
20-40f13030f1
40-6032501600
60-80f27070f2
80-10019901710
TotalΣf = f1 + f2 + 68Σfx = 3480 + 30f1 + 70f2

Given,

Σf = 120

⇒ f1 + f2 + 68 = 120

⇒ f1 + f2 = 120 - 68

⇒ f1 + f2 = 52

⇒ f1 = 52 - f2 ……….(1)

By formula,

Mean = ΣfxΣf\dfrac{Σfx}{Σf}

Substituting values we get :

50=3480+30f1+70f21206000=3480+30f1+70f2\Rightarrow 50 = \dfrac{3480 + 30f1 + 70f2}{120} \\[1em] \Rightarrow 6000 = 3480 + 30f1 + 70f2

Substituting value of f1 from equation (1) in above equation, we get :

⇒ 6000 = 3480 + 30(52 - f2) + 70f2

⇒ 6000 = 3480 + 1560 - 30f2 + 70f2

⇒ 6000 = 5040 + 40f2

⇒ 40f2 = 6000 - 5040

⇒ 40f2 = 960

⇒ f2 = 96040\dfrac{960}{40} = 24.

⇒ f1 = 52 - f2 = 52 - 24 = 28.

Hence, f1 = 28 and f2 = 24.

Answered By

1 Like


Related Questions