Question 40
Daily wages of 110 workers, obtained in a survey, are tabulated below:

Q 40.jpg



Compute the mean daily wages and modal daily wages of these workers.

Question 40 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Part 2

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.