Answer

Verified

345.9k+ views

**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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE