Harmonic mean refers to the reciprocal of arithmetic mean of the reciprocal of sum given numbers.

Question

ScanSolve AI Tutor · Accepted Answer

The problem asks to calculate the Harmonic Mean (HM) for the given set of numbers. Based on your partial work, the numbers are $4, 6, 8$ . The formula for the Harmonic Mean is given as $\text{HM} = \frac{n}{\sum \frac{1}{x}}$ .

Identify the given numbers and the count.
The numbers are $x = \{4, 6, 8\}$ .
The count of numbers is $n = 3$ .
Calculate the reciprocal of each number.
$\frac{1}{4}, \frac{1}{6}, \frac{1}{8}$
Sum the reciprocals of the numbers.
To sum these fractions, find a common denominator, which is 24.
$\sum \frac{1}{x} = \frac{1}{4} + \frac{1}{6} + \frac{1}{8} = \frac{6}{24} + \frac{4}{24} + \frac{3}{24} = \frac{6+4+3}{24} = \frac{13}{24}$
Your calculation for the sum of reciprocals is correct.
Substitute the sum of reciprocals and the count into the Harmonic Mean formula.
$\text{HM} = \frac{n}{\sum \frac{1}{x}} = \frac{3}{\frac{13}{24}}$
Simplify the expression.
To divide by a fraction, multiply by its reciprocal.
$\text{HM} = 3 \times \frac{24}{13} = \frac{72}{13}$
Convert the fraction to a decimal.
$\text{HM} \approx 5.538$
The Harmonic Mean for the given set of numbers is:
$5.538$

Harmonic mean refers to the reciprocal of arithmetic mean of the reciprocal of sum given numbers.

Answer

Step-by-step solution

Identify the given numbers and the count.

Calculate the reciprocal of each number.

Sum the reciprocals of the numbers.

Substitute the sum of reciprocals and the count into the Harmonic Mean formula.

Simplify the expression.

Convert the fraction to a decimal.

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