EX 13.3 (Question: 5)

EX 13.3 (Question: 5) The following table gives the distribution of the life time of 400 neon lamps : Life time (in hours) Number of lamps 1500 - 2000 14 2000 - 2500 56 2500 - 3000 60 3000 - 3500 86 3500 - 4000 74 4000 - 4500 62 4500 - 5000 48 Find the median life time of a lamp.

Solution: Total number of neon lamps = 400 = "n/2" = 200. Cumulative frequency just greater than 200 = 216 So, the median class is 3000 – 3500Here, Lower limit 𝑙=3000 Cumulative frequency before median class 𝑐𝑓=130 Frequency of median class 𝑓=86 Class width ℎ=500Using formula: Median = 𝑙 + ( "n/2−c𝑓" /"𝑓" )"×h" Where: 𝑙 = 3000, c𝑓 = 130, 𝑓 = 86, ℎ = 500. Median = 3000 + ("(200−130 " /86)"× 500" "=" 3000 + 70/86 "×500" "=" 3000 + 406.98 =3406.98 hours Median life time = 3406.98 hours

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