Question

The mean of 5 observation is 19 Find the firth observation if four observation are 16, 18, 15
and 12​

Answer 1

Given:

• Mean of 5 observations = 19
• Observations: 16, 18, 15, 12, x

To find:

1. Fifth observation = x = ?

Method:

$\sf{Mean = \dfrac{Sum\: of \: all \: observations}{Total \: Number \: of \: Observations}}\\\\\\\implies \sf{19 = \dfrac{16 + 18+15+12+x}{5}}\\\\\\\implies \sf{19 = \dfrac{61 + x}{5} }\\\\\\\implies \sf{19 \times 5 = 61+x}\\\\\\\implies \sf{95 = 61+x}\\\\\\\implies \sf{x = 95 - 61}\\\\\\\implies \boxed{\large{\bf{x = 34}}}$

∴ Fifth Observation = 34

Answer 2

${\underline{\frak{\blue{question: }}}}$

• To find a fifth observation in a data.

${\frak{\underline{\blue{answer: }}}}$

Given :

• Mean of 5 observations = 19

• 4 observations are 16,18,15,12

Let , fifth observation be x,

• To find mean :

${\boxed{\underline{\bf{mean \: = \frac{total \: observations}{no.of \: observations} }}}}$

$\longrightarrow\sf\small \: \frac{16 + 18 + 15 + 12 + x }{5} = 19 \\ \\ \longrightarrow\sf\small \small \frac{61 + x}{5} = 19 \\ \\ \longrightarrow\sf \small \: 61 + x = 19 \times 5 \\ \\ \longrightarrow\sf \: 61 + x = 95 \\ \\ \longrightarrow\sf \: x = 95 - 61 \\ \\ \bf\longrightarrow \: x = 34$

So, fifth observation is 34.

Let's verify::

$: \implies\sf \frac{16 + 18 + 15 + 12 + 34}{5} = 19 \\ \\ \sf\ : \implies \: \frac{95}{5} = 19 \\ \\ : \implies \sf \: 19 = 19$

$\bf \: LHS \: = \: RHS \:$

Thus Solved !!