Find the mode of the following data.

xi	0-10	10-20	20-30	30-40	40-50	50-60
fi	2	4	6	8	10	12

Given:

xi: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60

fi: 2, 4, 6, 8, 10, 12

Formula used:

Mode = L + ((f_m - f₁) / (2f_m - f₁ - f₂)) × h

Where,

L = Lower boundary of the modal class

f_m = Frequency of the modal class

f₁ = Frequency of the class preceding the modal class

f₂ = Frequency of the class succeeding the modal class

h = Class interval

Calculation:

Modal class = 50-60

L = 50

f_m = 12

f₁ = 10

f₂ = 0 (since there is no class after 50-60)

h = 10

Mode = 50 + ((12 - 10) / (2 × 12 - 10 - 0)) × 10

⇒ Mode = 50 + (2 / 14) × 10

⇒ Mode = 50 + (1/7) × 10

⇒ Mode = 50 + (10 / 7) 

⇒ Mode = 50 + 1.43

⇒ Mode = 51.43

∴ The correct answer is option 1 (51.43).