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Quiz grades Joey鈥檚 first 14 quiz grades in a marking period were \(\begin{array}{lllllll}{86} & {84} & {91} & {75} & {78} & {80} & {74} \\ {87} & {76} & {96} & {82} & {90} & {98} & {93} \\ \hline\end{array}\) Calculate the mean. Show your work. Interpret your result in context.

Short Answer

Expert verified
The mean of Joey's quiz grades is approximately 85.

Step by step solution

01

Sum of the Grades

Add up all the quiz grades Joey received. Work through each number: 86 + 84 + 91 + 75 + 78 + 80 + 74 + 87 + 76 + 96 + 82 + 90 + 98 + 93.
02

Total Calculation

Compute the total sum from Step 1. The sum is 86 + 84 + 91 + 75 + 78 + 80 + 74 + 87 + 76 + 96 + 82 + 90 + 98 + 93 = 1190.
03

Count the Number of Grades

Determine how many quiz grades Joey has. Count each grade listed, which is 14.
04

Calculate the Mean

Find the average of the quiz scores by dividing the sum of the scores by the number of grades.The mean is \( \frac{1190}{14} \approx 85 \).
05

Interpret the Result

The mean score of approximately 85 indicates that, on average, Joey scored an 85 on his quizzes in this marking period.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quiz Grades Analysis
When analyzing quiz grades, we need to take a close look at all the individual scores Joey received. These scores represent his performance over several quizzes throughout a marking period. By examining the grades:
  • 86, 84, 91, 75, 78, 80, 74
  • 87, 76, 96, 82, 90, 98, 93
We gain insight into the range of Joey鈥檚 quiz scores. Some are quite high, like 98 and 96, while others are lower, such as 74 and 75. Each of these marks plays a role in the overall evaluation of his performance. Understanding this distribution is key to grasping how his average, or mean score, comes about. By gathering all these grades, you form the basis for calculating Joey鈥檚 average performance.
Statistical Interpretation
Interpreting statistical data, like Joey's quiz scores, involves understanding what the mean value represents. First, we calculated Joey's mean quiz score, which was approximately 85. This provides a benchmark:
  • The mean tells us the central tendency, or the average score, across all quizzes.
  • It helps identify how Joey's performance generally looks across the board for these 14 quizzes.
  • By comparing this mean to individual scores, we can evaluate consistency or recognize occasional high and low scores.
Understanding what the mean signifies aids in assessing performance patterns. In Joey's case, even though some quiz scores are quite varied, the mean reflects an overall consistent performance level within his academic framework.
Average Score Calculation
Calculating an average score is a straightforward yet impactful way of understanding data. To find the mean of Joey鈥檚 quizzes, follow these steps:
1. **Total Sum:** Start by adding all quiz scores: \[ 86 + 84 + 91 + 75 + 78 + 80 + 74 + 87 + 76 + 96 + 82 + 90 + 98 + 93 = 1190 \]
2. **Counting Scores:** Find out how many scores there are, which in Joey's case is 14 quizzes.
3. **Compute the Mean:** Use the formula for the mean: \( \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Scores}} \) \[ \text{Mean} = \frac{1190}{14} \approx 85 \]This calculated mean is not just a number; it reflects how Joey generally performed in these quizzes. It is a handy way of summarizing data to give an overall picture of performance without scrutinizing each score individually.

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