The standard deviation of 10, 16, 10, 16, 10, 10, 16, 16 is

Option c: 3. Solution: Given data: 10, 16, 10, 16, 10, 10, 16, 16; n = 8 Count: Four 10s and four 16s. Step 1: Calculate Mean. x-bar = 4 x 10 + 4 x 16/8 = 40 + 64/8 = 104/8 = 13 Step 2: Calculate squared deviations. - For the four 10s: (10 - 13)^2 = 9; total = 4 x 9 = 36 - For the four 16s: (16 - 13)^2 = 9; total = 4 x 9 = 36 sum(xi - x-bar)^2 = 36 + 36 = 72 Step 3: Calculate Variance. sigma^2 = 72/8 = 9 Step 4: Calculate SD. sigma = sqrt(9) = 3 So SD = 3 (Option C). The given correctoption 'b' (6) is incorrect. Hence, Option C is the correct answer.

The standard deviation of $10, 16, 10, 16, 10, 10, 16, 16$ is

The correct answer is Option c: $3$. **Given data:** 10, 16, 10, 16, 10, 10, 16, 16; $n = 8$ Count: Four 10s and four 16s. **Step 1: Calculate Mean.** $$\bar{x} = \frac{4 \times 10 + 4 \times 16}{8} = \frac{40 + 64}{8} = \frac{104}{8} = 13$$ **Step 2: Calculate squared deviations.** - For the four 10s: $(10 - 13)^2 = 9$; total = $4 \times 9 = 36$ - For the four 16s: $(16 - 13)^2 = 9$; total = $4 \times 9 = 36$ $$\sum(x_i - \bar{x})^2 = 36 + 36 = 72$$ **Step 3: Calculate Variance.** $$\sigma^2 = \frac{72}{8} = 9$$ **Step 4: Calculate SD.** $$\sigma = \sqrt{9} = 3$$ So SD = **3** (Option C). The given `correct_option` 'b' (6) is incorrect. Hence, **Option C** is the correct answer.

Central Tendency & DispersionMTP Apr 21Question 3171 of 473

All Questions

The standard deviation of $\displaystyle 10, 16, 10, 16, 10, 10, 16, 16$ is

Options

\displaystyle 4

\displaystyle 6

\displaystyle 3

\displaystyle 0

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Correct Answer

✅ Option c — $\displaystyle 3$

All Options:

A $\displaystyle 4$
B $\displaystyle 6$
C $\displaystyle 3$
D $\displaystyle 0$

Detailed Solution & Explanation

**Given data:** 10, 16, 10, 16, 10, 10, 16, 16;

\displaystyle n = 8

Count: Four 10s and four 16s. **Step 1: Calculate Mean.**

\bar{x} = \frac{4 \times 10 + 4 \times 16}{8} = \frac{40 + 64}{8} = \frac{104}{8} = 13

**Step 2: Calculate squared deviations.** - For the four 10s:

\displaystyle (10 - 13)^2 = 9

; total =

\displaystyle 4 \times 9 = 36

- For the four 16s:

\displaystyle (16 - 13)^2 = 9

; total =

\displaystyle 4 \times 9 = 36

\sum(x_i - \bar{x})^2 = 36 + 36 = 72

**Step 3: Calculate Variance.**

\sigma^2 = \frac{72}{8} = 9

**Step 4: Calculate SD.**

\sigma = \sqrt{9} = 3

So SD = **3** (Option C). The given `correct_option` 'b' (6) is incorrect. Hence, **Option C** is the correct answer.

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The standard deviation of 10,16,10,16,10,10,16,16\displaystyle 10, 16, 10, 16, 10, 10, 16, 1610,16,10,16,10,10,16,16 is