A population has a mean of $\mu$ = $9$ and a sum of scores $\Sigma x$ = $54$. How many scores are in the population?

• A. $54$
• B. $63$
• C. $6$
• D. $9$

Answer: (C)

Verified step by step guidance

1. Recall the formula for the mean of a population: \(\mu = \frac{\sum x}{N}\), where \(\mu\) is the mean, \(\sum x\) is the sum of all scores, and \(N\) is the number of scores in the population.
2. Identify the given values: the mean \(\mu = 9\) and the sum of scores \(\sum x = 54\).
3. Substitute the known values into the mean formula: \$9 = \frac{54}{N}$.
4. To find \(N\), multiply both sides of the equation by \(N\) to get \$9N = 54$.
5. Solve for \(N\) by dividing both sides by 9: \(N = \frac{54}{9}\).