Question

Find the mode and median for 35,32,35,42,38,32,34​

Answer 1

$\Large\frak{\underline{\underline{Correct \: Question:}}}$

35,32,35,42,38,32,34

Find the Mean,Median and Mode of data.

$\rule{170}2$

$\Large\frak{\underline{\underline{Your~Answer:}}}$

$\underline{\bigstar\:\textsf{Mean \: of \: data:}}$

$\maltese\:\:\:\boxed{\normalsize\sf\ Mean = \frac{Sum \: of \: all \: observations}{Number \: of \: total \: observations}}\\\\\\\normalsize\ : \implies\sf\ Mean = \scriptsize\frac{(35,32,35,42,38,32,34)}{7}\\\\\\\normalsize\ : \implies\sf\ Mean = \frac{\cancel{248}}{\cancel{7}}\\\\\\\normalsize\ : \implies\sf\ Mean = 35.42\\\\\\\normalsize\ : \implies{\underline{\boxed{\sf \red{ Mean = 35.42}}}}$

$\underline{\bigstar\:\textsf{Median \: of \: data:}}\\ \\ \normalsize\sf\bullet\: Arrange \: the \: data \: into \: ascending \: order:\\ 32,32,34,35,35,38,42\\ns(n) = 35 = odd \: number \\\\\maltese\:\:\boxed{\sf\ Median = \frac{n +1}{2}^{th} \: term}\\\\\\\normalsize\ : \implies\sf\ Median = \frac{35 + 1}{2}^{th} \: term\\\\\\\normalsize\ : \implies\sf\ Median = \frac{\cancel{36}}{\cancel{2}}^{th} \: term\\\\\\\normalsize\ : \implies\sf\ Median = 8^{th} \: term\\\\\\\normalsize\ : \implies\sf\ Median = 72\\\\\\\normalsize\ : \implies{\underline{\boxed{\sf \red{Median = 72 }}}}$

$\underline{\bigstar\:\textsf{Mode \: of \: data:}}\\\\ \sf\ Reference \: of \: occuring \: of \: outcomes \: is \\ \sf\ shown \: in \: table:$

$\boxed{\begin{tabular}{ c || c} \bf{Observation} & \bf{Times of occurring}\\ \cline{1-2}\sf{32} & \sf{2} \\ \cline{1-2}\sf{34} & \sf{1}\\ \cline{1-2}\sf{35} & \sf{2}\\ \cline{1-2}\sf{38} & \sf{1}\\ \cline{1-2}\sf{42} & \sf{1}\\ \end{tabular}}$

$\normalsize\sf\ From \: the \: observations \: it \: is \: quite \: simple \: \\ \sf\ to \: know \: that \: 32(2)and\:35(2)\: has \: highest \: times \: of \: occurring \\\\\\\maltese\:\:\boxed{\sf\ Mode = Maximum \: number \: of \: occuring}\\\\\\ \normalsize\ : \implies\sf\ Mode = 32\:and\:52 \\\\\\\normalsize\ : \implies{\underline{\boxed{\sf \red{ Mode = 32\:and\:35}}}}$

Answer 2

Correct Question :

Find the mean, median and mode for 35,32,35,42,38,32,34.

Answer :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Mean of the data:

Mean of data = $\sf\frac{Sum\: of \: all \: observations}{Total \: Observations}$

Mean = $\sf\frac{35+32+35+42+38+32+34}{7}$

Mean = $\sf\frac{248}{7}$

Mean = $\sf\frac{\cancel{248}}{\cancel{7}}$

Mean = 35.4

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Median of the data:

Median = The number that comes in between the data.

Arrange the data in ascending order :–

32, 32, 34, 35, 35, 38, 42

Median = $\sf\frac{n+1^th}{2}$

Median = $\sf\frac{35+1^th}{2}$

Median = $\sf\frac{\cancel{36^th}}{\cancel{2}}$

Median = $\sf{8^th\: term}$

Median = 72

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Mode of the data:

Mode = The number that comes more times in the given data.

The given table shows the number that occurs more time :–

$\boxed{\begin{tabular}{ c || c} \bf{Observation} & \bf{Times of occurring}\\ \cline{1-2}\sf{32} & \sf{2} \\ \cline{1-2}\sf{34} & \sf{1}\\ \cline{1-2}\sf{35} & \sf{2}\\ \cline{1-2}\sf{38} & \sf{1}\\ \cline{1-2}\sf{42} & \sf{1}\\ \end{tabular}}$

Mode = 32 and 35