Question

find the median of the data c-I 50-60,60,-70,70-80, 80-90, 90-100 F=12 ,14,8,6,10​

Answer 1

$\begin {tabular} { | c | c | c | }</p><p>\cline { 1-3 } C.I & Frequency & Cumulative\: frequency \\</p><p>\cline { 1-3 } 50-60 & 12 & 12(cf) \\</p><p>\cline { 1-3 } 60-70 & 14(f)& 26 \\</p><p>\cline { 1-3} 70-80 & 8 & 34 \\</p><p>\cline { 1-3 } 80-90 & 6 & 40 \\</p><p>\cline { 1-3 } 90 - 100 & 10& 50 \\</p><p>\cline {1-3} \_& n = 50 & \_ \\</p><p>\cline { 1-3 } \end { tabular }$

$Here \: \frac{n}{2} = 25$

$60 - 70 \:is \: the \:class \:whose \: cumulative \\frequency \:is \: greater \:than \:25$

$So, 60 - 70 \: is \:the\: median \:class$

$l = 60, \: n = 50 , \: cf = 12 , \: f = 14 ,\:h = 10$

$\boxed { \pink { Median = l + \big( \frac{\frac{n}{2} - cf }{f} \big)\times h }}$

$Median = 60 + \big ( \frac{\frac{50}{2} - 12}{14}\big) \times 10 \\= 60 + \frac{25-12}{14} \times 10 \\= 60 + \frac{130}{14}\\= 60 + 9.29 \\= 69.29$

Therefore.,

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

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