Ex 15.1, 7 - Find mean deviation about median - Chapter 15 - Mean deviation about median - Discrete Frequency

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  1. Chapter 15 Class 11 Statistics
  2. Serial order wise
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Ex15.1, 7 Find the mean deviation about the median for the data. The given observations are already in ascending order.Adding a column corresponding to cumulative frequencies of the given data, we obtain the following table. c.f = cumulative frequency N = 26 (even) ∴ Median = ((𝑁/2)^𝑡ℎ 𝑡𝑒𝑟𝑚 +(𝑁/2 + 1)^𝑡ℎ 𝑡𝑒𝑟𝑚)/2 = ((26/2)^𝑡ℎ 𝑡𝑒𝑟𝑚 + (26/2 +1)^𝑡ℎ 𝑡𝑒𝑟𝑚)/2 = (〖13〗^𝑡ℎ 𝑡𝑒𝑟𝑚 +〖14〗^𝑡ℎ 𝑡𝑒𝑟𝑚 )/2 As both observations lie in the c.f of 14 13th term = 14th term = 7 ∴ Median = (7 + 7 )/2=13 ∑128▒𝑓𝑖 = 26 ∑128▒𝑓𝑖 |𝑥𝑖 −M| = 84 ∴ Mean Deviation = (Σ 𝑓_𝑖 |𝑥_(𝑖 − M) |)/𝑓_𝑖 = 84/26 = 3.23

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