Question 40 Daily wages of 110 workers, obtained in a survey, are tabulated below: Compute the mean daily wages and modal daily wages of these workers.
Daily Wages No. of workers
100 – 120 10
120 – 140 15
140 – 160 20
160 – 180 22
180 – 200 18
200 – 220 12
220 – 240 13
Here ui = (𝑥𝑖 − 𝑎)/ℎ
Where a = assumed mean = 170
Now,
Mean(𝑥 ̅) = a + h × (∑▒𝑓𝑖𝑢𝑖)/(∑▒𝑓𝑖)
Where a = assumed mean = 170
h = Class interval = 20
∑▒𝑓𝑖 = 110
∑▒𝑓𝑖𝑢𝑖 = 1
Putting values
Mean(𝑥 ̅) = a + h × (∑▒𝑓𝑖𝑢𝑖)/(∑▒𝑓𝑖)
Mean(𝑥 ̅) = 170 + 20 × 1/110
𝑥 ̅ = 170 + 0.18
𝑥 ̅ = 170.18
∴ Mean Daily wages is Rs 170.18
Finding Mode
Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h
Modal class = Interval with highest frequency
= 160 – 180
Where l = lower limit of modal class
h = class-interval
f1 = frequency of the modal class
f0 = frequency of the class before modal class
f2 = frequency of the class after modal class
Mode = 160 + (22 − 20)/(2(22) − 20 − 18) × 20
= 160 + 2/(44 − 38) × 20 = 160 + 2/6 × 20 = 160 + 6.67 = 166.67
Daily Wages No. of workers
100 – 120 10
120 – 140 15
140 – 160 20
160 – 180 22
180 – 200 18
200 – 220 12
220 – 240 13
∴ Modal Daily wages is Rs 166.67

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.