Question

The following data gives the information on the observed lifetimes (in hours) of 287

electric bulbs.

Lifetimes (in hours) 0-20 20-40 40-60 60-80 80-100 100-

120

Number of electric bulbs 26 31 35 42 82 71

Determine the modal lifetimes of the bulbs​

Answer 1

Lifetime(in hours) No. of components 0-20 10 20-40 35 40-60 52 60-80 61 80-100 38 100-120 29 As frequency is maximum for the class 60−80, modal class is 60−80.Mode=l+ 2f 1 −(f 0+f 2 )f 1 −f 0×hwhere,l = lower limit of modal class =60f 1 = frequency of modal class =61f 0 = frequency of class preceding the modal class =52f 2 = frequency of class succeding the modal class =38 h= higher limit - lower limit =80−60=20

= higher limit - lower limit =80−60=20Mode=60+ 2×61−(52+38)61−52 ×20

= higher limit - lower limit =80−60=20Mode=60+ 2×61−(52+38)61−52 ×20⇒mode=60+ 329 ×20=60+5.625=65.625

9 ×20=60+5.625=65.625Hence, the modal lifetimes of the components are 65.625 hrs.

Answer 2

this solution is right

other solution given above is wrong