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# The mean height of 12 men is 1.70 m, and the mean height of 8 women is 1.60 m. Find the total height of the 12 men, the total height of the 8 women, the mean height of the 20 men and women.

Last updated date: 13th Jul 2024
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Hint: Here the question belongs to the topic of mean or average. We have to find the mean height of both men and women. To solve this First, we have to multiply the average height of men with the total number of men. We get the total height of men similarly for women. Next by considering the total height of both men and women, we can determine the mean or average height of both men and women. This will be a required solution.

Complete step by step solution:
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
To calculate it: add up all the numbers, then divide by how many numbers there are.
Consider the given question,
The mean height of 12 men $= 1.70\,m$
Therefore, the total height of 12 men $= 12 \times 1.70 = 20.4\,m$
The mean height of 8 women $= 1.60\,m$
Therefore, the total height of 8 women $= 8 \times 1.60 = 12.8\,m$
Now, find the mean height of 20 men and women
The formula for the mean is given by
$mean = \,\dfrac{{Sum\,\,of\,\,total\,\,heights\,\,of\,\,men\,\,and\,\,women}}{{Total\,\,no.\,\,of\,\,both\,\,men\,\,and\,\,women}}$
Therefore, we have
$\Rightarrow mean = \,\dfrac{{20.4 + 12.8}}{{20}}$
On adding all the terms in the numerator, we have
$\Rightarrow mean = \,\dfrac{{33.2}}{{20}}$
On dividing the number 33.2 by 20 we have
$\Rightarrow mean = \,1.66$
Therefore, the mean height of 20 men and women is 1.66 m.
So, the correct answer is “1.66 m”.

Note: To solve these kinds of problem the Student’s must know the formula of mean i.e., $mean = \,\dfrac{{sum\,\,of\,\,all\,\,numbers}}{{no.\,\,of\,numbers}}$. Remember If we know two any parameters of the formula of mean we can determine the unknown parameter by simple arithmetic operation between two known parameters.