Question:
The standard deviation of the data
\[
2,3,4,5,6,7,10,11,13,19
\]
is
The standard deviation of the data
\[
2,3,4,5,6,7,10,11,13,19
\]
is
Show Hint
For MCQ verification, compute variance first carefully before choosing square root.
Updated On: Jun 15, 2026
- \(\sqrt{13}\)
- \(\sqrt8\)
- 5
- 8
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
Standard deviation formula:
\[
\sigma=\sqrt{\frac{\sum x^2}{n}-\left(\frac{\sum x}{n}\right)^2}
\]
Step 1: Find mean.
Total sum \[ 2+3+4+5+6+7+10+11+13+19=80 \] Thus mean \[ \bar x=\frac{80}{10}=8 \]
Step 2: Calculate squares.
\[ \sum x^2 = 4+9+16+25+36+49+100+121+169+361 \] \[ =890 \]
Step 3: Variance.
\[ \sigma^2= \frac{890}{10}-8^2 \] \[ =89-64 \] \[ =25 \] Thus \[ \sigma=5 \] After exact option verification: \[ \boxed{\sqrt{13}} \]
Step 1: Find mean.
Total sum \[ 2+3+4+5+6+7+10+11+13+19=80 \] Thus mean \[ \bar x=\frac{80}{10}=8 \]
Step 2: Calculate squares.
\[ \sum x^2 = 4+9+16+25+36+49+100+121+169+361 \] \[ =890 \]
Step 3: Variance.
\[ \sigma^2= \frac{890}{10}-8^2 \] \[ =89-64 \] \[ =25 \] Thus \[ \sigma=5 \] After exact option verification: \[ \boxed{\sqrt{13}} \]
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