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# Example 15 110 the following table gives the

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Unformatted text preview: lculate median income Solution: Cumulative Income group Number of frequency (Class-interval) workers c.f (Frequency) 1 1 Below 100 21 20 100-150 63 42 150-200 118 55 200-250 180 62 250-300 225 45 300-350 255 30 350-400 280 25 400-450 295 15 450-500 313 18 500-550 323 10 550-600 325 2 600 and above 325 111 N 325 =162.5 = 2 2 Here l = 250, N = 325, f = 62, c = 50, m = 118 162.5 − 118 Md = 250+ × 50 62 = 250+35.89 = 285.89 Example 16: Calculate median from the following data Value Frequency 0-4 5 True 20-24 5-9 10-14 f 15-19 class 8 Value 10 12interval 7 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 5 8 10 12 7 6 3 2 53 0.5-4.5 4.5-9.5 9.5-14.5 14.5-19.5 19.5-24.5 24.5-29.5 29.5-34.5 34.5-39.5 c.f 25-29 6 30-34 3 5 13 23 35 42 48 51 53 53 N = = 26.5 2 2 N −m Md = l + 2 ×c f 26.5 − 23 ×5 12 = 14.5+1.46 = 15.96 = 14.5 + Example 17: Following are the daily wages of workers in a textile. Find the median. 112 35-39 2 Wages ( in Rs.) less than 100 less than 200 less than 300 less than 400 less than 500 less than 600 less than 700 less than 800 less than 900 less than 1000 Number of workers 5 12 20 32 40 45 52 60 68 75 Solution : We are given upper limit and less than cumulative frequencies. First find the class-intervals and the frequencies. Since the values are increasing by 100, hence the width of the class interval equal to 100. Class interval 0-100 100-200 200-300 300- 400 400-500 500-600 600-700 700-800 800-900 900-1000 f c.f 5 7 8 12 8 5 7 8 8 7 75 5 12 20 32 40 45 52 60 68 75 N 75 = = 37.5 2 2 113 N 2 −m Md = l + × c f 37.5 − 32 = 400 + × 100 = 400 + 68.75 = 468.75 8 Example 18: Find median for the data given below. Marks Number of students 70 Greater than 10 62 Greater than 20 50 Greater than 30 38 Greater than 40 30 Greater than 50 24 Greater than 60 17 Greater than 70 9 Greater than 80 4 Greater than 90 Solution : Here we are given lower limit and more than cumulative frequencies. Class interval f More than c.f Less than c.f 8 70 8 10-20 20 62 12 20-30 32 50 12 30-40 40-50 8...
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