Verified answer

Answer:

f = 12

Step-by-step explanation:

For the table refer to the attachement.

Mode = 45

so, modal class = 40 - 60

We have,

L = 40

H = 20

f₁ = f

f₀ = 10

f₂ = 6

⇒ Mode = L + (f₁ - f₀)H / (2f₁ - f₀ - f₂)

⇒ 45 = 40 + (f - 10)20 / (2f - 10 - 6)

⇒ 5 = (f - 10)20 / (2f - 16)

⇒ 1/4 = (f - 10) / (2f - 16)

⇒ 2f - 16 = 4f - 40

⇒ 2f = 24

⇒ f = 12

The missing frequency is 12 cm.