Calculate the Harmonic Mean of $1, \frac{1}{3}, \frac{1}{6}$ and $\frac{1}{9}$.
(A) 2.48
(B) 0.21
(C) 0.31
(D) 0.25

Question

Accepted Answer

> [!TLDR]
> HM = n ÷ (sum of reciprocals) = 4 ÷ 19 = 0.21.

### Step 1 — Formula
$$HM = \frac{n}{\sum \frac{1}{x_i}}$$

### Step 2 — Reciprocals of the values
For $x = 1, 	frac13, 	frac16, 	frac19$:
$$\frac{1}{1}=1,\quad \frac{1}{1/3}=3,\quad \frac{1}{1/6}=6,\quad \frac{1}{1/9}=9$$
Sum of reciprocals $= 1 + 3 + 6 + 9 = 19$, with $n = 4$.

### Step 3 — Compute the HM
$$HM = \frac{4}{19} = 0.2105 \approx 0.21$$ …

Harmonic Mean

The governing formula

Why it works

Worked illustration …

Step 1 — Formula

Step 2 — Reciprocals of the values

Step 3 — Compute the HM

Step 1 — Formula

Step 2 — Reciprocals of the values

Step 3 — Compute the HM

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