Math Problem Statement

what is the average percent of this set of percentages? 100% 0% 82% 100% 88% 50% 60% 79% 83% 86% 78% 65% 98% 96% 52% 92% 83% 68% 88% 70% 60% 68% 85% 86% 80% 83% 98% 100% 67% 60% 103% 73% 0% 60% 75% 37% 88% 75% 72% 73% 75% 68% 83% 80% 75% 85% 90% 48% 90% 70% 75% 90% 83% 98% 40% 90% 0% 78% 53%

Solution

To calculate the average percentage of this data set, we add up all the values and then divide by the total number of entries. Here is the step-by-step calculation:

  1. Sum of all percentages: Add each percentage value.
  2. Count of values: Find the total number of entries.
  3. Average calculation: Divide the sum by the count.

Let's proceed with these steps:

Step 1: Sum of All Percentages

The total sum of all percentages in the list is 4626%4626\%.

Step 2: Count of Values

There are 57 values in total.

Step 3: Average Calculation

Average=Sum of all valuesNumber of values=46265781.16%\text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{4626}{57} \approx 81.16\%

Final Answer

The average percentage is approximately 81.16%.

Would you like a breakdown of this process or have any questions?


Here are five questions related to this topic:

  1. How would the average change if the highest value was removed?
  2. What is the median of this data set?
  3. How does the inclusion of 0% values affect the average?
  4. What is the range of percentages in this data set?
  5. How would you calculate a weighted average if each percentage had a different weight?

Tip: Always check for outliers or unusually high/low values that might skew the average.

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Math Problem Analysis

Mathematical Concepts

Statistics
Averages

Formulas

Average = Sum of all values / Number of values

Theorems

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Suitable Grade Level

Grades 6-8