Question

What is the median for the following observations?
5, 8, 6, 9, 11, 4.
(a) 6
(b) 7
(C) 8
(d) None of these​

Answer 1

Required Answer:-

(b) 7 ✔

Explanation:-

Arrange the given data/observations in ascending order:-

4, 5, 6, 8, 9, 11

Number of observations(n) = 6 (even digit).

So,

$\large{\sf \longmapsto \: Median = \dfrac{ \bigg( \dfrac{n}{2} \bigg)^{th} \: obs. \: + \bigg( \dfrac{n}{2} + 1\bigg)^{th} \: obs. }{2} } \\ \\ \\ \large{ \sf \longmapsto \: Median = \dfrac{ \bigg( \dfrac{6}{2} \bigg)^{th} \: obs. \: + \bigg( \dfrac{6}{2} + 1\bigg)^{th} \: obs. }{2}} \\ \\ \\ \large{\sf \longmapsto \: Median = \dfrac{3 {}^{th} obs. \: + \: 4 {}^{th} obs.}{2}} \\ \\ \\ \large{\sf \longmapsto \: median = \dfrac{6 + 8}{2}} \\ \\ \\ \large{\sf \longmapsto \: Median = \dfrac{14}{2}} \\ \\ \\ \large{\sf \longmapsto \: \underline{\underline{\purple{Median = 7}}}}$

Hence, Median of the given observation is 7.

Related Formula:-

• When n is even:-

ㅤㅤMedian = $\sf\bigg( \dfrac{n}{2} + 1\bigg)^{th} \: obs.$

• When n is odd:-

ㅤㅤMedian = $\sf\dfrac{ \bigg( \dfrac{n}{2} \bigg)^{th} \: obs. \: + \bigg( \dfrac{n}{2} + 1\bigg)^{th} \: obs. }{2}$

Answer 2

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ The given all the observations are given as 5, 8, 6, 9, 11, 4

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ Median of the given observation.

Some options are given for help -

6, 7, 8 and none of these.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Median of the given observation = 7

${\large{\bold{\rm{\underline{Knowledge \; required}}}}}$

Median - Medianof a data is the middle number when the data has been arranged in ascending or descending order.

How to find median ? To find the median of the data, we have to arrange the given data in either ascending order or descending order.

Some more information - There are two differ - differ ways of finding the median based on the number of observation.

• In the case of an odd number of observation, the median is the middle term of arranged data.

• For an even number of observation, the median is the average of the two middle term (divide by 2) (have to add the two terms first)

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Using all the above information let's solve this question properly..!

Let's arrange the observation in ascending order firstly..!

Given observation = 5, 8, 6, 9, 11, 4.

Ascending order = 4, 5, 6, 8, 9, 11.

Now it's already cleared that the total terms are 6. Means it's even so we have to take two midde terms and have to divide it by 2 and have to add..!

➝ Middle two terms = 6 and 8

➝ Median = ${\sf{\dfrac{6+8}{2}}}$

➝ Median = ${\sf{\dfrac{14}{2}}}$

➝ Median = ${\sf{7}}$

${\frak{\bull Henceforth, \: 7 \: is the \: median \: of \: given \: observation}}$