Ex 14.3, 5 - Chapter 14 Class 10 Statistics

Transcript

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 − 2000 14 14 2000 − 2500 56 14 + 56=70 2500 − 3000 60 70+60=130 3000 − 3500 86 130 + 86=216 3500 − 4000 74 216 + 74=290 4000 − 4500 62 290 + 62=352 4500 − 5000 48 352 + 48= 400 Median = l + (𝑛/2 −𝑐𝑓)/𝑓 × h n = ∑▒𝑓𝑖 = 400 𝑛/2 = 400/2 = 200 ∴ 3000 – 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 + (𝑛/2 −𝑐𝑓)/𝑓 × h = 3000 + (200 −130)/86 × 500 = 3000 + 70/86 × 500 = 3000 + 406.98 = 3406.98 So, median life of lamp is 3406.98 hours