Question

please answer this plzzzzzzzzzzzz​

Answer 1

Answer:

MODE = Sum of observation

No. of observation

10+35+22+16+18+29/6

= 130/6

= 21.66. ANS.

Answer 2

Answer:

The mode of the given data is 33.16 years (approx.).

Step-by-step-explanation:

We have given the lifetimes of people and their frequencies.

We have to find the mode of the given data.

$\begin{array}{|c|c|}\cline{1-2}\sf\:Class\:(\:Lifetimes\:) & \sf\:Frequency\\\cline{1-2}\sf\:0 - 20 & \sf\:10\:\rightarrow\:f_0\\\cline{1-2}\boxed{\sf\: 20 - 40} & \boxed{\sf\:35\:\rightarrow\:f_1}\\\cline{1-2}\sf\:40 - 60 & \sf\:22\:\rightarrow\:f_2\\\cline{1-2}\sf\:60 - 80 & \sf\:16\\\cline{1-2}\sf\:80 - 100 & \sf\:18\\\cline{1-2}\sf\:100 - 120 & \sf\:29\\\cline{1-2}\end{array}$

From the above table, the highest frequency is 35.

Hence, the modal class of the data is 20 - 40.

Now,

$\bullet\sf\:Lower\:class\:limit\:of\:modal\:class\:(\:L\:)\:=\:20\\\\\\\bullet\sf\:Frequency\:of\:modal\:class\:(\:f_1\:)\:=\:35\\\\\\\bullet\sf\:Frequency\:of\:the\:class\:preceding\:the\:modal\:class\:(\:f_0\:)\:=\:10\\\\\\\bullet\sf\:Frequency\:of\:the\:class\:succeeding\:the\:modal\:class\:(\:f_2\:)\:=\:22\\\\\\\bullet\sf\:Class\:interval\:of\:the\:modal\:class\:(\:h\:)\:=\:20$

Now, we know that,

$\pink{\sf\:Mode\:=\:L\:+\:\bigg[\:\dfrac{f_1\:-\:f_0}{2f_1\:-\:f_0\:-\:f_2}\:\bigg]\:\times\:h}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:Mode\:=\:20\:+\:\bigg[\:\dfrac{35\:-\:10}{2\:\times\:35\:-\:10\:-\:22}\:\bigg]\:\times\:20\\\\\\\implies\sf\:Mode\:=\:20\:+\:\bigg[\:\dfrac{25}{70\:-\:32}\:\bigg]\:\times\:20\\\\\\\implies\sf\:Mode\:=\:20\:+\:\dfrac{25}{\cancel{38}}\:\times\:\cancel{20}\\\\\\\implies\sf\:Mode\:=\:20\:+\:\dfrac{25}{19}\:\times\:10\\\\\\\implies\sf\:Mode\:=\:20\:+\:\dfrac{250}{19}\\\\\\\implies\sf\:Mode\:=\:\dfrac{20\:\times\:19\:+\:250}{19}\\\\\\\implies\sf\:Mode\:=\:\dfrac{380\:+\:250}{19}\\\\\\\implies\sf\:Mode\:=\:\dfrac{630}{19}\\\\\\\implies\sf\:Mode\:=\:33.157\\\\\\\implies\boxed{\red{\sf\:Mode\:\approx\:33.16\:years}}$

The mode of the given data is 33.16 years (approx.).