Find the median lifetime of a lamp.

Solution:

Class Interval      Frequency           Cumulative

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

Information:

n = 400 &n/2 = 200

Middle class = 3000 – 3500

Hence, l = 3000, Cf = 130,

f = 86 and h = 500

\[\begin{array}{*{35}{l}}

   ~  \\

   Middle\text{ }=\text{ }3000\text{ }+\text{ }\left( \left( 200-130 \right)/86 \right)\text{ }\times \text{ }500  \\

\end{array}\]

\[=\text{ }3000\text{ }+\text{ }\left( 35000/86 \right)\]

\[=\text{ }3000\text{ }+\text{ }406.97\]

\[=\text{ }3406.97\]

Hence, the middle life season of the lights = 3406.97 hours