The following table gives the distribution of the life time of 400 neon lamps. Find the median life time of a lamp.

Question :

Life time (in hours)Number of lamps
1500 – 200014
2000 – 250056
2500 – 300060
3000 – 350086
3500 – 400074
4000 – 450062
4500 – 500048

Solution :

First, we prepare the following table to compute the median :

Life time (in hours)Number of lampsCumulative frequency
1500 – 20001414
2000 – 25005670
2500 – 300060130
3000 – 350086216
3500 – 400074290
4000 – 450062352
4500 – 500048400

We have : n = 400 So, \(n\over 2\) = 200

The cumulative frequency just greater than \(n\over 2\) is 216 and the corresponding class is (3000 – 3500). Thus, it is the median class.

Here, l = 3000, cf = 130, f = 86 and h = 500.

Substituting these values in the formula,

Median = l + (\({n\over 2} – cf\over f\))\(\times\)h, we have :

Median = 3000 + \(70\over 86\) \(\times\) 500 = 3000 + 406.98 = 3406.98

Hence, median life time is 3406.98 hours.

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