Question

Calculate the mode from the following data

Class	50-60	60-70	70-80	80-90	90-100	100-110	110-120
frequ-ency	8	10	16	14	10	5	2

1. 67.5
2. 77.5
3. 87.5
4. 76

Answer 1

Correct Answer - Option 2 : 77.5

Concept:

Mode of the given frequency table

Mode = L + \(\left [\frac{f_1~-~f_o}{2f_1~-~f_o~-~f_2} \right ] × h\)

Where,

L = lowest class of highest frequency, f₁ = Highest frequency, f2 = second highest frequency, f₀ = third highest frequency,

h = Class difference.

Given:

L = 70, f1 = 16, f₂ = 14, f₃ = 10, h = 70 - 80 = 10.

Calculation:

Mode = L + \(\left [\frac{f_1~-~f_o}{2f_1~-~f_o~-~f_2} \right ] × h\)

= 70 + \(\left [\frac{16~-~10}{2~×16~-~10~-~14} \right ] × 10\)

= 70 + \(\frac{6}{8}\) × 10

= 70 + 7.5

= 77.5