Find the variance of a group of data whose standard deviation is 12.34 to the nearest whole number.

Analyze the question: You are given the standard deviation (12.34) and asked for the variance, rounded to the nearest whole number.

Concept: Variance is the square of the standard deviation:

Variance = (Standard deviation)²

Solution:

Variance = (12.34)²

Break it down:

• 12² = 144
• 2 × 12 × 0.34 = 8.16
• 0.34² = 0.1156

Variance = 144 + 8.16 + 0.1156 = 152.2756

To the nearest whole number: 152

Answer: Option C (152).

Tip: Whenever a question gives the standard deviation and asks for the variance, just square it. If it gives the variance and asks for the standard deviation, take the square root. For quick squaring, use (a + b)² = a² + 2ab + b², as above. Roughly, 12.34² is a bit more than 12² = 144 and a bit less than 13² = 169, so 152 is a sensible result.