Question

The standard deviation of the data \[ 2,3,4,5,6,7,10,11,13,19 \] is

• A. \(\sqrt{13}\)
• B. \(\sqrt8\)
• C. 5
• D. 8

Hint:

For MCQ verification, compute variance first carefully before choosing square root.

Answer 1

The Correct Option is A

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: \[ \boxed{\sqrt{13}} \]