Question

Compute the mode from the following series:

Size	45 – 55	55 – 65	65 – 75	75 – 85	85 – 95	95 – 105	105 - 115
Frequency	7	12	17	30	32	6	10

Answer 1

As the class 85 – 95 has the maximum frequency, it is the modal class.
Now, `x_k = 85, h = 10, f_k = 32, f_(k-1) = 30, f_(k+1) = 6`
∴ Mode, `M_0 = x_k + {ℎ × ((f_k− f_(k−1)))/((2f_k− f_(k−1)−f_(k+1)))}`
`= 85 + {10 × ((32−30))/((2×32−30−6))}`
`= 85 + {10 × 2/28}`
= (85 + 0.71)
= 85.71
Hence, mode = 85.71