Question

find the unknown entries
​

Answer 1

$\Large\underline{\textsf{\textbf{\purple{ \mapsto Given:}}}}$

A frequency distribution table is given to us .

$\Large\underline{\textsf{\textbf{\purple{ \mapsto To\:Find:}}}}$

The values of a , b , c , d , e & f from the table .

$\Large\underline{\textsf{\textbf{\purple{ \mapsto Answer:}}}}$.

$\underline{\red{\sf Given\: table\: to\: us \:is :- }}$

$\begin{tabular}{|c|c|c|}\cline{1-3} \bf Height (in cm ) &\bf Frequency &\bf Cummulative Frequency \\\cline{1-3} 150-155 &12&a\\\cline{1-3} 155-160 & b & 25 \\\cline{1-3} 160- 165 & 10 & c \\\cline{1-3} 165 - 170 & d & 43 \\\cline{1-3} 170 - 175 & e & 48 \\\cline{1-3} 175 - 180 & 2 & f \\\cline{1-3} \bf Total & 50 & \\\cline{1-3}\end{tabular}$

As we know that Cummulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors . So , here ;

$\sf \bullet Value \:of\:a\: will\:be\:12.$

$\blue{\sf \underline{Also , \:here \:we\: can\: find\: rest \:as, }}$

$\tt:\implies a + b = 25 \\\\\tt:\implies 12 + b = 25 \\\\\tt:\implies b = 25 - 12 \\\\\underline{\boxed{\red{\tt\longmapsto b = 13 }}}$

$\rule{200}2$

$\tt:\implies 25+ 10= c \\\\\underline{\boxed{\red{\tt\longmapsto c = 35 }}}$

$\rule{200}2$

$\tt:\implies c + d = 43 \\\\\tt:\implies 35 + d = 43 \\\\\tt:\implies d = 43 - 35 \\\\\underline{\boxed{\red{\tt\longmapsto d= 8 }}}$

$\rule{200}2$

$\tt:\implies 43+e=48 \\\\\tt:\implies e = 48-43 \\\\\tt:\implies e= 5 \\\\\underline{\boxed{\red{\tt\longmapsto e= 5 }}}$

$\rule{200}2$

$\tt:\implies 48+2=f \\\\\underline{\boxed{\red{\tt\longmapsto f=50 }}}$

$\underline{\purple{\sf Hence \:the\:final\: table\: would\:be :-}}$

$\begin{tabular}{|c|c|c|}\cline{1-3} \bf Height (in cm ) &\bf Frequency &\bf Cummulative Frequency \\\cline{1-3} 150-155 &12&12\\\cline{1-3} 155-160 & 13 & 25 \\\cline{1-3} 160- 165 & 10 & 35 \\\cline{1-3} 165 - 170 & 8 & 43 \\\cline{1-3} 170 - 175 & 5 & 48 \\\cline{1-3} 175 - 180 & 2 & 50 \\\cline{1-3} \bf Total & 50 & \\\cline{1-3}\end{tabular}$

Answer 2

$\Large\underline{\textsf{\textbf{\purple{ \mapsto Given:}}}}↦Given:</p><p></p><p>A frequency distribution table is given to us .</p><p></p><p>\Large\underline{\textsf{\textbf{\purple{ \mapsto To\:Find:}}}}↦ToFind:</p><p></p><p>The values of a , b , c , d , e & f from the table .</p><p></p><p>\Large\underline{\textsf{\textbf{\purple{ \mapsto Answer:}}}}↦Answer: .</p><p></p><p>\underline{\red{\sf Given\: table\: to\: us \:is :- }}Giventabletousis:−</p><p></p><p>\begin{gathered}\begin{tabular}{|c|c|c|}\cline{1-3} \bf Height (in cm ) &\bf Frequency &\bf Cummulative Frequency \\\cline{1-3} 150-155 &12&a\\\cline{1-3} 155-160 & b & 25 \\\cline{1-3} 160- 165 & 10 & c \\\cline{1-3} 165 - 170 & d & 43 \\\cline{1-3} 170 - 175 & e & 48 \\\cline{1-3} 175 - 180 & 2 & f \\\cline{1-3} \bf Total & 50 & \\\cline{1-3}\end{tabular}\end{gathered}</p><p></p><p>As we know that Cummulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors . So , here ;</p><p></p><p>\sf \bullet Value \:of\:a\: will\:be\:12.∙Valueofawillbe12.</p><p></p><p>\blue{\sf \underline{Also , \:here \:we\: can\: find\: rest \:as, }}Also,herewecanfindrestas,</p><p></p><p>\begin{gathered}\tt:\implies a + b = 25 \\\\\tt:\implies 12 + b = 25 \\\\\tt:\implies b = 25 - 12 \\\\\underline{\boxed{\red{\tt\longmapsto b = 13 }}}\end{gathered}:⟹a+b=25:⟹12+b=25:⟹b=25−12⟼b=13</p><p></p><p>\rule{200}2</p><p></p><p>\begin{gathered}\tt:\implies 25+ 10= c \\\\\underline{\boxed{\red{\tt\longmapsto c = 35 }}}\end{gathered}:⟹25+10=c⟼c=35</p><p></p><p>\rule{200}2</p><p></p><p>\begin{gathered}\tt:\implies c + d = 43 \\\\\tt:\implies 35 + d = 43 \\\\\tt:\implies d = 43 - 35 \\\\\underline{\boxed{\red{\tt\longmapsto d= 8 }}}\end{gathered}:⟹c+d=43:⟹35+d=43:⟹d=43−35⟼d=8</p><p></p><p>\rule{200}2</p><p></p><p>\begin{gathered}\tt:\implies 43+e=48 \\\\\tt:\implies e = 48-43 \\\\\tt:\implies e= 5 \\\\\underline{\boxed{\red{\tt\longmapsto e= 5 }}}\end{gathered}:⟹43+e=48:⟹e=48−43:⟹e=5⟼e=5</p><p></p><p>\rule{200}2</p><p></p><p>\begin{gathered}\tt:\implies 48+2=f \\\\\underline{\boxed{\red{\tt\longmapsto f=50 }}}\end{gathered}:⟹48+2=f⟼f=50</p><p></p><p>\underline{\purple{\sf Hence \:the\:final\: table\: would\:be :-}}Hencethefinaltablewouldbe:−</p><p></p><p>\begin{gathered}\begin{tabular}{|c|c|c|}\cline{1-3} \bf Height (in cm ) &\bf Frequency &\bf Cummulative Frequency \\\cline{1-3} 150-155 &12&12\\\cline{1-3} 155-160 & 13 & 25 \\\cline{1-3} 160- 165 & 10 & 35 \\\cline{1-3} 165 - 170 & 8 & 43 \\\cline{1-3} 170 - 175 & 5 & 48 \\\cline{1-3} 175 - 180 & 2 & 50 \\\cline{1-3} \bf Total & 50 & \\\cline{1-3}\end{tabular}\end{gathered}</p><p></p><p>$