Question

Find the mode of the following frequency distribution ​

Answer 1

Answer:

mode = 67

Step-by-step explanation:

$\begin{gathered}\boxed {\begin{array}{c|c|c|c|c|c|c |c }\bf {Class\:} &\sf 0 - 15 & \sf 15 - 30&\sf 30 - 45 &\sf 45 - 60 & 60 - 75&\sf75 - 90& \sf 90 - 105\\&&&&&&&\\ \bf Frequency &\sf 4 &\sf 5&\sf 23 &\sf 45 &\sf 66&\sf 42& \sf15 \\&&&&&&\\ \end {array}}\end{gathered}$

$\blue{\huge\underline{\underline{\qquad\qquad Solution \qquad \qquad}}}$

$\sf \: Largest \: Frequency \: is \: \red{ 66 } \: it \: is \: in \: class \: \: \red{60 - 75 }$

$❒ \: \sf \ell = lowar \: limit \: of \: the \: model \: class \implies \green{ 60 }$

$❒ \: \: \sf C = size \: of \: class \: interval \: \implies \green{15}$

$❒ \: \: \sf f_1 = Frequency \: of \: the \: model \: class \: \implies \green{66} \:$

$❒ \: \: \sf f_0=Frequency \: of \: the \: class \: \sf preceding \: the \: modal \: c lass \implies \green{45}$

$❒ \: \: \sf f_2=Frequency \: of \: the \: class \: \sf \: suceding \: \: the \: modal \: c lass \implies \green{42}$

_____________________________

Mode is dinner denoted bi capital Z

$\sf formula \: of \: mode \longrightarrow \pink{\boxed{ Z =\ell +\bigg\lgroup \dfrac{f_1-f_0}{2f_1-f_0-f_2}\bigg\rgroup ×C}}</p><p>$

♤substituting the values we get,

$: \tt\longrightarrow Z =\ell +\bigg\lgroup \dfrac{f_1-f_0}{2f_1-f_0-f_2}\bigg\rgroup ×C \\ \\ \\ \\ \tt :\longrightarrow Z =60 +\bigg\lgroup \dfrac{66 - 45}{2(66) - 45 - 42}\bigg\rgroup ×15 \\ \\ \\ \\ : \tt\longrightarrow Z =60 + \bigg\lgroup \dfrac{21}{132 - 87}\bigg\rgroup \times 15 \\ \\ \\ \\ \tt : \longrightarrow \: Z = 60 + \bigg \lgroup \dfrac{21}{45} \bigg \rgroup \times 15 \\ \\ \\ \\ \tt : \longrightarrow \: Z = 60 + \dfrac{21 \times 15}{45} \\ \\ \\ \\ \tt : \longrightarrow \: Z = 60 + \dfrac{ \cancel{315}}{ \cancel{45} } \\ \\ \\ \\ \tt : \longrightarrow \: Z = 60 +7 \\ \\ \\ \\ \tt : \longrightarrow \: Z = 67$

♤The mode of the following Frequency = 67 ♤

Answer 2

Answer:

refer to the above attachment