On 6 quizzes Joe scored 73,88,86,90, 87 and 29. What is the mean and standard deviation. On the 7th quiz he scored 32 - how does this affect the mean and standard deviation?

Let's break this problem into two parts:

1. **Mean and Standard Deviation of the First Six Quizzes:**
   Joe's scores on the first six quizzes are: 73, 88, 86, 90, 87, and 29.

2. **Effect on Mean and Standard Deviation After Adding the 7th Quiz:**
   Joe's 7th quiz score is 32, and we will analyze how it affects both the mean and standard deviation.

### Step 1: Calculate the Mean and Standard Deviation of the First Six Quizzes
- **Mean**: The mean is the average of the scores, calculated as:
  \[
  \text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of quizzes}}
  \]
  For the first six quizzes:
  \[
  \text{Mean} = \frac{73 + 88 + 86 + 90 + 87 + 29}{6}
  \]

- **Standard Deviation**: The standard deviation is a measure of how much the scores vary from the mean. It is calculated using the formula:
  \[
  \text{Standard Deviation} = \sqrt{\frac{1}{N} \sum (x_i - \mu)^2}
  \]
  where \( N \) is the number of scores, \( x_i \) are the individual scores, and \( \mu \) is the mean.

### Step 2: Recalculate the Mean and Standard Deviation After Adding the 7th Quiz Score
Now, after adding the 7th score (32), the new set of scores becomes: 73, 88, 86, 90, 87, 29, 32. We will calculate the new mean and standard deviation for this set.

I will calculate both the initial values and the values after adding the 7th quiz score.### Results:

1. **For the first six quizzes**:
   - **Mean**: 75.5
   - **Standard Deviation**: 21.52

2. **After adding the 7th quiz (score = 32)**:
   - **New Mean**: 69.29
   - **New Standard Deviation**: 25.07

### Effect of the 7th Quiz Score:
- The **mean** has decreased from 75.5 to 69.29 due to the low score of 32.
- The **standard deviation** has increased from 21.52 to 25.07, indicating a larger spread in the quiz scores, mainly because the 7th score is far from the earlier average.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How does removing the lowest score affect the mean and standard deviation?
2. What would happen to the mean if Joe scores 100 on the next quiz?
3. How do we interpret the significance of the standard deviation in this case?
4. How does the variance relate to standard deviation in this example?
5. What are other measures of central tendency besides the mean?

**Tip**: A high standard deviation suggests a wide range of scores, while a low standard deviation indicates that the scores are clustered closely around the mean.

On 6 quizzes Joe scored 73, 88, 86, 90, 87, and 29. What is the mean and standard deviation? On the 7th quiz he scored 32 - how does this affect the mean and standard deviation?

Learn how to calculate the mean and standard deviation for quiz scores, and understand the impact of adding a new quiz score of 32 on the overall statistics. This problem uses key concepts in statistics and is suitable for students in Grades 9-12.

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