On 6 quizzes Joe scored 73,88,86,90, 87 and 29. What is the mean and standard deviation

To calculate the mean and standard deviation for Joe's quiz scores, we proceed as follows:

### 1. **Calculating the Mean:**
The mean (average) is calculated by summing all the scores and then dividing by the number of quizzes.

Given scores: 73, 88, 86, 90, 87, 29

\[
\text{Mean} = \frac{73 + 88 + 86 + 90 + 87 + 29}{6} = \frac{453}{6} = 75.5
\]

### 2. **Calculating the Standard Deviation:**
The standard deviation measures how much the scores vary from the mean.

**Step 1:** Find the differences from the mean for each score:
- \(73 - 75.5 = -2.5\)
- \(88 - 75.5 = 12.5\)
- \(86 - 75.5 = 10.5\)
- \(90 - 75.5 = 14.5\)
- \(87 - 75.5 = 11.5\)
- \(29 - 75.5 = -46.5\)

**Step 2:** Square each difference:
- \((-2.5)^2 = 6.25\)
- \((12.5)^2 = 156.25\)
- \((10.5)^2 = 110.25\)
- \((14.5)^2 = 210.25\)
- \((11.5)^2 = 132.25\)
- \((-46.5)^2 = 2162.25\)

**Step 3:** Find the average of these squared differences:
\[
\text{Variance} = \frac{6.25 + 156.25 + 110.25 + 210.25 + 132.25 + 2162.25}{6} = \frac{2777.5}{6} \approx 462.92
\]

**Step 4:** Take the square root of the variance to find the standard deviation:
\[
\text{Standard Deviation} \approx \sqrt{462.92} \approx 21.52
\]

### **Final Answers:**
- **Mean:** 75.5
- **Standard Deviation:** 21.52

Would you like more details on how these calculations were performed, or do you have any other questions?

---

**Related Questions:**
1. How would the mean and standard deviation change if Joe's lowest score was dropped?
2. What is the median score of Joe's quizzes?
3. How does the standard deviation help in understanding the consistency of Joe's quiz scores?
4. What would the variance be if Joe's scores were closer to each other?
5. How would adding another quiz score of 75 affect the mean and standard deviation?

**Tip:** The standard deviation is a useful measure of spread, indicating how much the values in a dataset differ from the mean.

Learn how to calculate the mean and standard deviation for Joe's quiz scores. This problem covers basic statistics, including mean calculation, standard deviation measurement, and variance. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation