Find the Harmonic Mean of 2, 4 & 6.
(A) 3.30
(B) 3.00
(C) 3.75
(D) 4.00

Question

Accepted Answer

> [!TLDR]
> $HM=\dfrac{n}{\sum(1/x)}=\dfrac{3}{11/12}=\dfrac{36}{11}\approx3.27\approx3.30$.

### Step 1 — Harmonic mean formula
> [!FORMULA]
> $$HM = \dfrac{n}{\sum \dfrac{1}{x_i}}$$

### Step 2 — Sum the reciprocals
$$\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6} = \dfrac{6+3+2}{12} = \dfrac{11}{12}.$$

### Step 3 — Divide
$$HM = \dfrac{3}{11/12} = 3	imes\dfrac{12}{11} = \dfrac{36}{11} \approx 3.27.$$
The nearest given value is $3.30$.

**Why the other options are wrong:** $3.00$ (B) would only arise from a different set; $4.00$ (D) is the arithmetic mean; $3.75$ (C) does not match the reciprocal computation. (Recall $HM\le GM\le AM$; here $AM=4$, so $HM<4$, ruling out (D).) …

Harmonic Mean

The governing formula

Why it works

Worked illustration …

Step 1 — Harmonic mean formula

Step 2 — Sum the reciprocals

Step 3 — Divide

Step 1 — Harmonic mean formula

Step 2 — Sum the reciprocals

Step 3 — Divide

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