A 10-item statistics quiz was given to 30 students. The table below gives the scores received along with the corresponding frequencies.
\begin{tabular}{|c|c|c|c|c|c|c|}\
\hline Score & 5 & 6 & 7 & 8 & 9 & 10 \
\hline Frequency & 1 & 2 & 5 & 5 & 7 & 10 \
\hline
\end{tabular}
What was the mean score on the quiz?
Answer (2)
Calculate the total score by multiplying each score by its frequency and summing the results: ( 5 × 1 ) + ( 6 × 2 ) + ( 7 × 5 ) + ( 8 × 5 ) + ( 9 × 7 ) + ( 10 × 10 ) = 255 .
Divide the total score by the number of students (30) to find the mean score: 30 255 .
Simplify the fraction to find the mean score: 8.5 .
The mean score on the quiz is 8.5 .
Explanation
Understand the problem We are given the scores of 30 students on a 10-item statistics quiz and their corresponding frequencies. Our goal is to find the mean score.
Calculate the total score To find the mean score, we first need to calculate the total score by multiplying each score by its frequency and summing the results.
Calculate the sum of scores The total score is calculated as follows: ( 5 × 1 ) + ( 6 × 2 ) + ( 7 × 5 ) + ( 8 × 5 ) + ( 9 × 7 ) + ( 10 × 10 ) = 5 + 12 + 35 + 40 + 63 + 100 = 255 So, the total score is 255.
Calculate the mean score Next, we divide the total score by the number of students, which is 30, to find the mean score: Mean score = Number of students Total score = 30 255 = 8.5 Therefore, the mean score is 8.5.
State the final answer The mean score on the quiz is 8.5.
Examples
In educational settings, calculating the mean score of a quiz helps teachers understand the overall performance of the class. For example, if a teacher finds that the mean score on a difficult quiz is low, they might decide to review the material or adjust their teaching methods. This calculation provides a quick and easy way to assess student understanding and identify areas where additional support may be needed. It also serves as a benchmark for comparing performance across different quizzes or classes.
The mean score on the statistics quiz is 8.5, calculated by first finding the total score (255) and then dividing by the number of students (30). This average can help assess overall student performance. In summary, mean score = 8.5.
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