Question

what is the mean mode and median of 22,32,34,35,36,39?​

Answer 1

Given Numbers

• 22,32,34,35,36,39

To find

• mean, median and mode

Mean

Formula used

$\\\pink{ \boxed{ \sf{{Mean=\cfrac{Sum \: of \: all \: observations}{Total \: Number \: of \: Observations}}}}}$

$\sf{→Mean=\dfrac{22+32+34+35+36+39}{6}}$

$\sf{→Mean=\dfrac{198}{6}}$

$\sf{→Mean=33}$

Median

• 22,32,34,35,36,39

We can see that number of observation (n) is even.

Formula used

$\\\begin{gathered} \sf{Median}\begin{cases}\sf{\:\;\; value \: of \: \left( \frac{n+1}{2}\right)^{th} observations \: if \: n \: is \: odd} \\ \\\sf{\;\;\; \cfrac{value \: of \: \left( \frac{n}{2}\right)^{th} observations + value \: of \: \left( \frac{n+1}{2}\right)^{th} observations} {2}\ if \ n \ is \ odd}\end{cases}\end{gathered}$

${ →\sf{Median= \: \dfrac{\left(\frac{6}{2} \right)th \: term + \: \left(\frac{6 + 2}{2} \right)th \: term}{2}}}$

${ →\sf{Median= \: \dfrac{\left(3 \right)th \: term + \: (4) \: th \: term}{2}}}$

${ →\sf{Median= \: \dfrac{34 + \: 35 }{2}}}$

${ →\sf{Median= \: \dfrac{69}{2}}}$

${→ \sf{Median= \: 34.5}}$

Mode

• 22,32,34,35,36,39

Formula used

$\\\pink{\boxed{\sf Mode= 3 Median-2 Mean }}$

$\\ →\sf Mode= (3×34.5)-(2×33)$

$\sf→ Mode= 103.5-66$

$\sf →Mode= 37.5$

• Mean of the observation= 33.
• Median of the observation=34.5.
• Mode of the observation= 37.5