Question

the harmonic mean for the numbers 2 3 5​

Answer 1

Harmonic mean of numbers is found using the formula:-

Harmonic Mean = $\dfrac{n}{\dfrac{1}{n_{1}} + \dfrac{1}{n_{2}} + \dfrac{1}{n_{3}}}$

So, the harmonic mean of these numbers would be:-

Harmonic Mean = $\dfrac{3}{\dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{5}}$

Harmonic Mean = $\dfrac{3}{\dfrac{15+10+6}{30}}$

Harmonic Mean = $\dfrac{3}{\dfrac{31}{30}}$

Harmonic Mean = $3 \div \dfrac{31}{30}$

Harmonic Mean = $3 \times \dfrac{30}{31}$

Harmonic Mean = $\dfrac{90}{31}$

Harmonic Mean = 2.9 (approx)

So, the Harmonic Mean of these numbers is 2.9 !

Answer 2

Answer: The harmonic mean for the numbers 2, 3 and 5​ is 2.9

Step-by-step explanation:

The harmonic mean is a type of average we use in mathematics, specifically using one of the Pythagorean means.
In some circumstances, where the average rate is preferred, it is appropriate.
The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations or numbers.

Here we will find the harmonic mean of 2, 3, and 5 .

Using the formula
$H={\frac {n}{{\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}+\cdots +{\frac {1}{x_{n}}}}}={\frac {n}{\sum \limits _{i=1}^{n}{\frac {1}{x_{i}}}}}=\left({\frac {\sum \limits _{i=1}^{n}x_{i}^{-1}}{n}}\right)^{-1}.}H={\frac {n}{{\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}+\cdots +{\frac {1}{x_{n}}}}}={\frac {n}{\sum \limits _{i=1}^{n}{\frac {1}{x_{i}}}}}=\left({\frac {\sum \limits _{i=1}^{n}x_{i}^{-1}}{n}}\right)^{-1}.}$

Here n= 3
$x_1$= 2

$x_2$ = 3
$x_3$ = 5

Now,
First step of finding Harmonic mean of 2,3 and 5=   $\frac{3}{\frac{1}{2} +\frac{1}{3} +\frac{1}{5} }$

Second step of finding Harmonic mean of 2,3 and 5=  $\frac{3}{\frac{15+10+6}{30} }$

Third step of finding Harmonic mean of 2,3 and 5= $3$÷$\frac{31}{30}$

Final step of Harmonic mean of 2,3 and 5= $3$×$\frac{30}{31}$ =$\frac{90}{31}$ = 2.9

Thus, the harmonic mean of 2, 3 and 5 is 2.9.

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