Question

The average height of 30 boys was calculated to be 150 cm. It was detected that later one value of 165 cm was wrongly copied as 135 cm for the computation of the mean. Find the correct mean.

plz give this answer with proper steps❤​

Answer 1

Answer:

The correct mean of the height is 149 cm.

Step-by-step explanation:

Given :

Total boys = 30

Average height = 150 cm

Wrong value = 165 cm

Correct value = 135 cm

To find :

The Correct mean

Solution :

★ $\textsf{\underline{\underline{Sum of total Observations : }}}$

$\mathsf{Number \: of \: Observations \times Mean}$

$\sf{\implies} \: 30 \times 150 \\ \\ \sf{\implies} \: 4500$

Sum of observations = 4500

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Subtract the wrong value : }}}$

$\sf{\implies} \: 4500 - 165 \\ \\ \sf{\implies} \: 4335$

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Add the correct value : }}}$

$\sf{\implies} \: 4335 + 135 \\ \\ \sf{\implies} \: 4470$

Sum of observations (correct value) = 4470

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Correct Mean :}}}$

$\boxed{\sf{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\sf{\implies} \: Mean = \dfrac{4470}{30} \\ \\ \sf{\implies} \: Mean = 149$

Mean = 149

$\therefore$ The correct mean of the height is 149 cm.