The annual profits of 30 shops in a complex are given as a 'more than or equal to' cumulative distribution: profit = 5 (lakhs) for 30 shops, = 10 for 28, = 15 for 16, = 20 for 14, = 25 for 10, = 30 for 7, = 35 for 3. Using the ogive method, the median profit (in lakhs of rupees) is:

Question

The annual profits of 30 shops in a complex are given as a 'more than or equal to' cumulative distribution: profit >= 5 (lakhs) for 30 shops, >= 10 for 28, >= 15 for 16, >= 20 for 14, >= 25 for 10, >= 30 for 7, >= 35 for 3. Using the ogive method, the median profit (in lakhs of rupees) is:

Accepted Answer

17.5. Class frequencies (difference of successive cumulative values): 5-10 -> 2, 10-15 -> 12, 15-20 -> 2, 20-25 -> 4, 25-30 -> 3, 30-35 -> 4, 35-40 -> 3 (total 30). Less-than cumulative frequencies: 2, 14, 16, 20, 23, 27, 30. Here N/2 = 15 first exceeds at the class 15-20 (cf jumps from 14 to 16), so 15-20 is the median class. Median = L + ((N/2 - cf)/f)*h = 15 + ((15 - 14)/2)*5 = 15 + 2.5 = 17.5 lakhs. On a graph this is where the two ogives intersect.

The annual profits of 30 shops in a complex are given as a 'more than or equal to' cumulative distribution: profit >= 5 (lakhs) for 30 shops, >= 10 for 28, >= 15 for 16, >= 20 for 14, >= 25 for 10, >= 30 for 7, >= 35 for 3. Using the ogive method, the median profit (in lakhs of rupees) is:

Solution

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