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Solution :

\boxed{\begin{array}{cccc}\sf <klux>LIFE</klux>\: time&\sf No.\:of\:lamps&\sf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf <klux>1500</klux>-2000&\sf 14&\sf 14 \\\\\sf 2000-2500 &\sf 56&\sf 15+56=70 \\\\\sf 2500-3000 &\sf 60 &\sf 70+60=130  \\\\\sf 3000-3500&\sf 86&\sf 130+86=216\\\\\sf 3500-4000 &\sf 74 &\sf 216+74=290 \\\\\sf 4000-4500 &\sf 62 &\sf 290+62=352 \\\\\sf 4500-5000 &\sf 48 &\sf 352+48=400\end{array}}

n = 400

n/2 = 400/2 = 200

Therefore, 3000-3500 is the median class

  • lower limit of median class (L) = 3000

  • CF of the class before median class = 130

  • Frequency of the median class = 86

\sf Median =\ l\ +\ \dfrac{\frac{n}{2}\ -\ cf}{f}\ \times\ h

\sf Median =\ 3000\ +\ \dfrac{200-130}{2}\ \times\ 500

\sf Median =\ 300\ +\ \dfrac{70}{86}\ \times\ 500

\sf Median = 300 + 406.98

\underline{\boxed{\gray{\bf Median = 3406.98}}}\red\bigstar

Therefore, median life of the 3406.98 .



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