Question

Hi there!

Solve the above question.
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Answer 1

Solution :

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

n = 400

n/2 = 400/2 = 200

Therefore, 3000-3500 is the median class

• lower limit of median class (l) = 3000

• Class interval (h) = 2000 - 1500 = 500

• 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 .

Answer 2

ANSWER:

☆ TABLE

$\begin{lgathered}\begin{tabular}{|c |c | c|}\cline{1-3}\bf \underline {Life Time(in hours) }&\bf\underline {Number of Lamps}&\bf\underline {Comulative frequency}\\\cline{1-3}\sf 1500-2000 & \sf 14 & \sf 14 \\\sf 2000-2500 & \sf 56 &\sf 14 + 56 = 70 \\\sf 2500-3000 &\sf 60 & \sf 70 + 60 = 130\\\sf 3000-3500 &\sf 86 &\sf 130 + 86 = 216\\\sf 3500-4000 & \sf 74 &\sf 216 + 74 = 290 \\\sf 4000-4500 &\sf 62 &\sf 290 + 62 = 352 \\\sf 4500-5000 &\sf 48 & \sf 352 + 48 = 400 \\\sf &\sf Total = 400 &\sf \\\cline{1-3}\end{tabular}\end{lgathered}$

SoluTion:-

As we know that,

$\maltese\;{\underline{\boxed{\bf{\pink{Median = l + \dfrac{ \frac{n}{2} - cf}{f} \times h}}}}}$

Total number of lamps (n) = 400

$\sf \dfrac{n}{2} = \cancel{ \dfrac{400}{2}} = 200$

$\therefore$ 3000 - 3500 is the median class

• l = lower limit of median class = 3000

• h = class interval = 2000 - 1500 = 500

• cf = cumulative frequency of the class before median class = 130

• f = frequency of median class = 86

Therefore,

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

$:\implies\sf 3000 + \frac{200 - 130}{86} \times 500$

$:\implies\sf 3000 + \frac{70}{86} \times 500$

$:\implies\sf 3000 + 406.98$

$:\implies\;{\underline{\boxed{\bf{\blue{3406.98}}}}}$

$\dag$ Hence, Median life of lamp is 3406.98 hours

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