Question

find the median of the following data. cl 50-60 60-70 70-80 80-90. 90-100. f 12 14. 8. 6. 10 ​

Answer 1

$\begin {tabular} {| c | c | c | } </p><p>\cline {1-3} class interval & frequency & cumulative frequency \\</p><p>\cline {1-3} 50 - 60 & 12 & 12 (cf)\\</p><p>\cline {1-3} 60 - 70 & 14 (f)& 26 \\</p><p>\cline {1-3} 70 - 80 & 8 & 34 \\</p><p>\cline {1-3} 80 - 90 & 6 & 40 \\</p><p>\cline {1-3} 90 - 100& 10& 50 \\</p><p>\cline {1-3} - & n=50 & - \\</p><p>\cline {1-3} </p><p>\end {tabular}$

$Here , n = 50 ,\: \frac{n}{2} = 25 , \\l = 60 ,\: c.f = 12, \\f = 14 , \: h = 10$

$\boxed { \pink { Median = l + \Big( \frac{\frac{n}{2} - c.f }{f} \Big) \times h }}$

$Median = 60 + \Big(\frac{ 25 - 12}{14} \Big) \times 10 \\= 60 + \frac{130}{14}\\= 60 + 9.29 \\= 69.29$

Therefore.,

$\red { Median }\green {= 69.29}$

•••♪