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Ex 15.1, 12 - Calculate mean deviation about median age for - Mean deviation about median - Continuous frequency distibution

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  1. Chapter 15 Class 11 Statistics
  2. Serial order wise
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Ex15.1, 12 Calculate the mean deviation about median age for the age distribution of 100 persons given below: Converting the given data in continuous frequency by subtracting 0.5 from lower age limit adding and 0.5 in upper limit N = ∑128▒𝑓𝑖 = 100 Median Class = (𝑁/2)^𝑡ℎterm = (100/2)^𝑡ℎ term = 50th term In above data, cumulative frequency of class 35.5 − 40.5 is 63 which is greater than 50. ∴ Median class = 35.5 − 40.5 Median = 𝑙 + ( 𝑁/2 − 𝐶)/𝑓 ×ℎ Where, 𝑙 = lower limits of median class N = sum of frequencies 𝑓 = frequency of median class C = Cumulative frequency of class before median class Here, 𝑙 = 35.5, N = 100, C = 37, ℎ = 5, 𝑓 = 26 Median = 35.5 + (100/2 −37)/26 × 5 = 35.5 + (50 − 37)/26 × 5 = 20 + 13/26 × 5 = 35.5 + 2.5 = 38 Now, ∑128▒𝑓𝑖 = 100 ∑128▒𝑓𝑖 |𝑥𝑖 −𝑀| = 735 ∴ Mean Deviation (M) = (∑▒〖 𝑓_𝑖 |𝑥𝑖 − M| 〗)/𝑓_𝑖 = 735/100 = 7.35

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