Kirk has the following four quiz scores (out of 
20
20​ points): 
17
,
15
,
15
,
18
17,15,15,18​

a) What is his mean quiz score?
Mean
Preview

b) Suppose Kirk has one more quiz coming up. What score must Kirk get on the next quiz to have a mean quiz score of 
16
16​ points?
Score needed
Preview


Let's solve each part of the problem step by step.

### Part (a) - Mean Quiz Score

Kirk's quiz scores are 17, 15, 15, and 18. The mean score is calculated by finding the sum of all the quiz scores and then dividing by the number of quizzes.

1. **Sum of quiz scores:**
   \[
   17 + 15 + 15 + 18 = 65
   \]

2. **Number of quizzes:**
   \[
   4
   \]

3. **Mean quiz score:**
   \[
   \text{Mean} = \frac{\text{Sum of quiz scores}}{\text{Number of quizzes}} = \frac{65}{4} = 16.25
   \]

So, Kirk's mean quiz score is **16.25**.

### Part (b) - Score Needed on the Next Quiz

Let's denote the score Kirk needs on the next quiz as \( x \). We want the mean of all five quizzes to be 16.

1. **Sum of the current quiz scores:**
   \[
   65
   \]

2. **Adding the score \( x \) for the next quiz:**
   \[
   65 + x
   \]

3. **Mean of all five quizzes should be 16:**
   \[
   \frac{65 + x}{5} = 16
   \]

4. **Solve for \( x \):**
   \[
   65 + x = 16 \times 5 = 80
   \]
   \[
   x = 80 - 65 = 15
   \]

So, Kirk must score **15** on the next quiz to achieve a mean quiz score of 16 points.

---

Would you like further details or have any questions? Here are 5 related questions to explore:

1. What would Kirk's mean score be if he scored 20 on the next quiz?
2. If Kirk scored 10 on the next quiz, what would his new mean score be?
3. How would the mean change if one of his current quiz scores was lower?
4. What is the range of his current quiz scores?
5. What is the median of Kirk's current quiz scores?

**Tip:** The mean is sensitive to each data point, so even one low or high score can significantly affect it.

Kirk has the following four quiz scores (out of 20 points): 17, 15, 15, 18. a) What is his mean quiz score? b) Suppose Kirk has one more quiz coming up. What score must Kirk get on the next quiz to have a mean quiz score of 16 points?

Learn how to calculate the mean quiz score for Kirk, who has quiz scores of 17, 15, 15, and 18. Additionally, determine the score Kirk needs on his next quiz to achieve an average score of 16 points. This problem covers essential statistical and algebraic concepts suitable for students in Grades 6-8.

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