Math Problem Statement

The table below shows the scores of a group of students on a 10-point quiz. The mean score on this test is:

Solution

The table shows test scores and their corresponding frequencies. To calculate the mean score, we'll use the formula for the mean of grouped dataThe table shows test scores and their corresponding frequencies. To calculate the mean score, we'll use the formula for the mean of grouped

Mean=(Test Score×Frequency)Frequency\text{Mean} = \frac{\sum (\text{Test Score} \times \text{Frequency})}{\sum \text{Frequency}}

Let's calculate the mean step-by-step:

  1. Multiply each test score by its frequency.
  2. Sum the results from step 1.
  3. Divide the total by the sum of frequencies.

Let's perform these calculations:

  • 3×2=63 \times 2 = 6
  • 4×6=244 \times 6 = 24
  • 5×2=105 \times 2 = 10
  • 6×3=186 \times 3 = 18
  • 7×3=217 \times 3 = 21
  • 8×2=168 \times 2 = 16
  • 9×2=189 \times 2 = 18
  • 10×2=2010 \times 2 = 20

Total of products: 6+24+10+18+21+16+18+20=1336 + 24 + 10 + 18 + 21 + 16 + 18 + 20 = 133

Now, sum the frequencies:

2+6+2+3+3+2+2+2=222 + 6 + 2 + 3 + 3 + 2 + 2 + 2 = 22

Finally, calculate the mean:

Mean=133226.05\text{Mean} = \frac{133}{22} \approx 6.05

So, the mean score on this test is approximately 6.05.

Would you like further details on the calculation or have any questions?

Here are 5 related questions for further practice:

  1. How would the mean change if the frequency of the score 10 increased by 1?
  2. What is the median score from this data set?
  3. How do you calculate the mode for this frequency table?
  4. What is the range of the scores from this table?
  5. How would the mean change if a score of 1 with a frequency of 1 was added to the table?

Tip: When dealing with frequency tables, always make sure to correctly multiply each category by its frequency before summing.

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Math Problem Analysis

Mathematical Concepts

Mean
Averages
Grouped Data

Formulas

Mean = (Sum of (Test Score × Frequency)) / (Sum of Frequencies)

Theorems

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Suitable Grade Level

Grades 7-9