Question

find the value of k for following distribution where mean is 16​

Answer 1

$\begin {tabular} {| c | c | c | c | }</p><p>\cline { 1-4 } Class & f_{1} & x_{i} & f_{i}x_{i} \\</p><p>\cline { 1-4 } 10 -12 & 12 & 11 & 132 \\</p><p>\cline { 1-4} 12-14 & 16 & 13 & 208 \\</p><p>\cline {1-4} 14-16 & 20 & 15 & 300 \\</p><p>\cline { 1-4 } 16-18 & 24 & 17 & 408 \\</p><p>\cline { 1-4 } 18-20 & k & 19 & 19k \\</p><p>\cline { 1-4 } 20-22 & 8 & 21 & 168 \\</p><p>\cline { 1-4 } 22 - 24 &4 & 23 & 92 \\</p><p>\cline { 1-4 } & \Sigma f_{i} = 84+k & \_& \Sigma f_{i}x_{i} = 360 + k \\</p><p></p><p>\cline {1-4} \end { tabular}$

$\overline {x} = 16\: (given)$

$\implies \frac{\Sigma f_{i}x_{i}}{\Sigma f_{i} } = 16$

$\implies \frac{1308 + 19k }{84+k} = 16$

$\implies 1308 + 19k = 16(84+k)$

$\implies 19k - 16k = 1344 - 1308$

$\implies 3k = 36$

$\implies k = 12$

Therefore.,

$\red { Value \:of \: k } \green { = 12 }$

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