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CBSE Class 10 Answered

the following table gives the distribution of the life time of 400 neon lamps 

life time(in hours)=1500-2000,2000-2500,2500-3000,3000-3500,3500-4000,4000-4500,4500-5000

numbers of lamps= 14,56,60,86,74,62,48

find the median life time of a lamp

Asked by akhilrallabandi08 | 19 Sep, 2021, 06:52: PM
Expert Answer
Lower value Upper value Number of lamps Cumulative Frequency
1500 2000 14 14
2000 2500 56 70
2500 3000 60 130
3000 3500 86 216
3500 4000 74 290
4000 4500 62 352
4500 5000 48 400
 
Since total number of lamps is 400, median class cumulative frequency is near to 200
 
From above table we see that median class is having lower value 2500 and upper value 3000
 
begin mathsize 14px style M e d i a n space equals space l space plus space fraction numerator begin display style n over 2 end style minus C f over denominator f end fraction cross times h end style
Where l = 3000 , lower value of median class,  n = 400 is total number of lamps ,
Cf = 130 is cumulative frequency of class previous to median class , f is frequency of median class
and h is class interval
 
Median = 3000 + [ ( 200 - 130) / 86 ] × 500 = 3407 
Answered by Thiyagarajan K | 19 Sep, 2021, 08:20: PM
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