Answer:
The class 35 - 40 has maximum frequency. So, it is the modal class.
From the given data,
- [tex]\sf \:\:\:\:\:\:\:\:\:\:x_{k}=35[/tex]
- [tex]\sf \:\:\:\:\:\:\:\:\:\:f_{k}=50[/tex]
- [tex]\sf \:\:\:\:\:\:\:\:\:\:f_{k-1}=34[/tex]
- [tex]\sf \:\:\:\:\:\:\:\:\:\:f_{k+1}=42[/tex]
- [tex]\sf \:\:\:\:\:\:\:\:\:\:h=5[/tex]
[tex] {\bf \:\: {By\:using\:the\: formula}} \\ \\ [/tex]
[tex]\:\dag\:{\small{\underline{\boxed{\sf {Mode,\:M_{o} =\sf\red{x_k + {\bigg(h \times \: \dfrac{ ( f_k - f_{k-1})}{ (2f_k - f_{k - 1} - f_{k +1})}\bigg)}}}}}}} \\ \\ [/tex]
[tex]\sf \:\:\:\:\:\:\:\:\:= 35+ {\bigg(5 \times \dfrac{(50 - 34)}{ ( 2 \times 50 - 34 - 42)}\bigg)} \\ \\ [/tex]
[tex]\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 35 +{\bigg(5 \times \dfrac{16}{24}\bigg)} \\ \\ [/tex]
[tex]\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= {\bigg(35+\dfrac{10}{3}\bigg)} \\ \\ [/tex]
[tex]\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:(35 + 3.33) =.38.33 \\ \\ [/tex]
[tex]\:\:\sf {Hence,}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \large{\underline{\mathcal{\gray{ mode\:=\:38.33}}}} \\ \\ [/tex]
[tex]{\large{\frak{\pmb{\underline{Additional\: information }}}}}[/tex]
MODE
- Most precisely, mode is that value of the variable at which the concentration of the data is maximum.
MODAL CLASS
- In a frequency distribution the class having maximum frequency is called the modal class.
[tex]{\bf{\underline{Formula\:for\: calculating\:mode:}}} \\ [/tex]
[tex]{\underline{\boxed{\sf {Mode,\:M_{o} =\sf\red{x_k + {\bigg(h \times \: \dfrac{ ( f_k - f_{k-1})}{ (2f_k - f_{k - 1} - f_{k +1})}\bigg)}}}}}} \\ \\ [/tex]
Where,
[tex]\sf \small\pink{ \bigstar} \: x_{k}= lower\:limit\:of\:the\:modal\:class\:interval.[/tex]
[tex] \small \blue{ \bigstar}[/tex][tex]\sf \: f_{k}=frequency\:of\:the\:modal\:class[/tex]
[tex]\sf \small\orange{ \bigstar}\: f_{k-1}=frequency\:of\:the\:class\: preceding\:the\;modal\:class[/tex]
[tex]\sf \small\green{ \bigstar}\: f_{k+1}=frequency\:of\:the\:class\: succeeding\:the\;modal\:class[/tex]
[tex] \small \purple{ \bigstar}[/tex][tex]\sf \: h= width \:of\:the\:class\:interval[/tex]
