Question

Following are the heights (in cm) of 8 students of a class, find the median.
104,110,98, 112, 124, 136, ,105,107​

Answer 1

Given: Heights of students (observations).

To find: The median.

Answer:

Observations: 104, 110, 98, 112, 124, 136, 105 and 107.

It's important to note that the observations must be arranged in the ascending order.

Observations (in order of ascendance)​: 98, 104, 105, 107, 110, 112, 124 and 136.

Formula to find the median:

$\sf \bigg(\dfrac{n\ +\ 1}{2}\bigg)th\ term,\ for\ when\ the\ number\ of\ observations\ is\ an\ odd\ number.$

 OR

$\sf \bigg(\dfrac{n}{2}\bigg)th\ +\ \bigg(\dfrac{n}{2}\ +\ 1\bigg)th\ term,\ for\ when\ the\ number\ of\ observations\ is\ an\ even\ number.$

Since the number of observations (n) given is an even number (8), the second formula will be used.

Equating the respective values,

$\sf Median\ =\ \bigg(\dfrac{8}{2}\bigg)th\ term\ +\ \bigg(\dfrac{8}{2}\ +\ 1\bigg)th\ term.\\ \\\\Median\ =\ 4th\ term\ +\ \bigg(4\ +\ 1\bigg)th\ term.\\\\\\Median\ =\ 4^t^h\ term\ +\ 5^t^h\ term.\\\\\\Median\ =\ 107\ +\ 110\\\\\\Median\ =\ 117.$

Answer 2

$\bf{ \huge{ \boxed {\tt{ \red{Answer \:: }}}}}$

Given :

The heights (in cm) of 8 students of a class are;

104, 110, 98, 112, 124, 136, 105, 107

To find :

The median.

Explanation :

We can arranged the ascending order above given observation.

98, 104, 105, 107, 110, 112, 124, 136.

The total number of observation (n) = 8 (even number).

Using formula of the median for even number, we get;

$\bf{ \large{ \boxed{ \sf{Median \: = \: \bigg( \frac{n}{2} \bigg)th \: term + \bigg( \frac{n}{2} + 1 \bigg)th \: term}}}}$

Therefore,

$\implies{ \sf{Median \: = \: \bigg( \dfrac{8}{2} \bigg)th \: term + \bigg( \dfrac{8}{2} + 1 \bigg)th \: term}} \\ \\ \\ \implies{ \sf{Median \: = \: \bigg( \cancel{ \frac{8}{2}} \bigg)th \: term + \bigg( \cancel{ \frac{8}{2}} + 1 \bigg)th \: term}} \\ \\ \\ \implies{ \sf{Median \: = \: 4th \: term + (4 + 1)th \: term}} \\ \\ \\ \implies{ \sf{Median \: = \: 4th \: term \: + \: 5th \: term}} \\ \\ \\ \implies{ \sf{Median \: = \: (107 + 110)}} \\ \\ \\ \implies{ \sf{ \red{Median \: = \: 117}}}$

Thus,

The median Is 117.