Question

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
Number of lamps 14 56 60 86 74 62 48
Find the median life time of a lamp.

Answer 1

Dear Student:

Life time (in hours)       Number of lamps    Cumulative Frequency(cf)

 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

                                    ∑fi = 400

$Median= l+\frac{\frac{n}{2}-cf }{f}*h$

Where, l =lower limit of median class=3000

            h=class interval=5000-4500=500

            n =∑fi

           f=frequency of the median class=86

          cf = cumulative frequency before median class=130

$Median= 3000+\frac{\frac{400}{2}-130 }{86}*500$

      Median  =3406.98

Answer 2

Thank you for asking this question. Here is your answer:

We will assume the mean to be A = 549.5

Mean, x = a + ( ∑fiui/ ∑fi x h)

= 649.5 + 57/200 x 100

= 649. 5 + 28.5

= 678

So the mean life span of the bulb is 678

If there is any confusion please leave a comment below.

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