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Worked Examples · Example 6
Q.

Calculate the mean deviation from the mean for the following distribution of the profits of companies.

Profits (₹ lakh)10–2020–3030–5050–7070–80
No. of companies (f)581683
Telangana TsbieTextbookSubjectiveImportance★★★★★est
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Mean =40.5= 40.5, ∑f∣d∣=519\sum f|d| = 519, so M.D.=51940=12.975M.D. = \dfrac{519}{40} = 12.975.

Step 1 — Mean. Using class mid-points mm: ∑fm=(5)(15)+(8)(25)+(16)(40)+(8)(60)+(3)(75)=75+200+640+480+225=1620\sum fm = (5)(15) + (8)(25) + (16)(40) + (8)(60) + (3)(75) = 75 + 200 + 640 + 480 + 225 = 1620, and ∑f=40\sum f = 40, so

Xˉ=∑fm∑f=162040=40.5\bar{X} = \dfrac{\sum fm}{\sum f} = \dfrac{1620}{40} = 40.5

Step 2 — Absolute deviations of mid-points from the mean, weighted by frequency.

C.I.fm.p.|d| = |m − 40.5|f|d|
10–2051525.5127.5
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