Given the following frequency distribution of quiz scores: Score: $5$, $6$, $7$, $8$; Frequency: $2$, $4$, $3$, $1$. What is the mean quiz score?

• A. $\frac{5\times 2+6\times 4+7\times 3+8\times 1}{2+4+3+1}=6.1$
• B. $7.0$
• C. $5.8$
• D. $6.5$

Answer: (A)

Verified step by step guidance

1. Identify the scores and their corresponding frequencies from the given data. Here, the scores are 5, 6, 7, and 8, and their frequencies are 2, 4, 3, and 1 respectively.
2. Calculate the total sum of all scores weighted by their frequencies. This means multiplying each score by its frequency and then adding all these products together. Mathematically, this is expressed as: \(\text{Sum} = 5 \times 2 + 6 \times 4 + 7 \times 3 + 8 \times 1\).
3. Calculate the total number of observations by adding all the frequencies together. This is: \(\text{Total Frequency} = 2 + 4 + 3 + 1\).
4. Compute the mean quiz score by dividing the weighted sum of scores by the total number of observations. The formula for the mean is: \(\text{Mean} = \frac{\text{Sum of (score \times frequency)}}{\text{Total Frequency}}\).
5. Interpret the result as the average quiz score based on the frequency distribution provided.