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

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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