Ex 14.3, 5 - Distribution of life time of 400 neon lamps - Median

  1. Chapter 14 Class 10 Statistics
  2. Serial order wise
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Ex 14.3, 5 Find the following table gives the distribution of the life time of 400 neon lamps: Find the median life time of a lamp. Life time (in hours) Number of lamps Cumulative frequency 1500 โˆ’ 2000 14 14 2000 โˆ’ 2500 56 14 + 56=70 2500 โˆ’ 3000 60 70+60=130 3000 โˆ’ 3500 86 130 + 86=216 3500 โˆ’ 4000 74 216 + 74=290 4000 โˆ’ 4500 62 290 + 62=352 4500 โˆ’ 5000 48 352 + 48= 400 Median = l + (๐‘›/2 โˆ’๐‘๐‘“)/๐‘“ ร— h n = โˆ‘โ–’๐‘“๐‘– = 400 ๐‘›/2 = 400/2 = 200 โˆด 3000 โ€“ 3500 is the median class l = lower limit of median class = 3000 h = class-interval = 2000 - 1500 = 500 cf = cumulative frequency of the class before median class = 130 f = frequency of the median class = 86 Median = l + (๐‘›/2 โˆ’๐‘๐‘“)/๐‘“ ร— h = 3000 + (200 โˆ’130)/86 ร— 500 = 3000 + 70/86 ร— 500 = 3000 + 406.98 = 3406.98 So, median life of lamp is 3406.98 hours

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