 If a sample of n = 9 scores, 8 of the scores are each above the mean by 1 point.  Where is the last score located relative to the mean?

To solve this problem, we can use the fact that the sum of the deviations from the mean of a sample must equal zero. This is because the mean is the balance point of the distribution, meaning the total deviation of all scores from the mean must cancel out to zero.

Given that there are 9 scores in the sample:

- 8 of the scores are each **1 point above the mean**, so the total deviation from the mean for these 8 scores is \( 8 \times 1 = 8 \) points above the mean.
- To balance this out, the remaining 1 score must have a deviation that brings the total deviation back to zero.

Let's denote the deviation of the 9th score from the mean as \( x \).

For the total deviation to be zero, the sum of all deviations must be:
\[
8 + x = 0
\]
Solving for \( x \):
\[
x = -8
\]

Therefore, the 9th score is **8 points below the mean**.

Would you like further clarification, or do you have any questions about this?

Here are some related questions to further your understanding:
1. How is the mean of a data set calculated?
2. What happens to the mean when you add or remove scores from the data set?
3. How would the location of the last score change if the first 8 scores were each 2 points above the mean?
4. How do deviations from the mean help in understanding the variance of a data set?
5. Can you explain how the sum of deviations from the mean is always zero?

**Tip:** Always remember that the sum of deviations from the mean is zero, as the mean represents the balance point of the data!

If a sample of n = 9 scores, 8 of the scores are each above the mean by 1 point. Where is the last score located relative to the mean?

Explore how to determine the location of the last score in a sample of 9 scores, where 8 scores are each 1 point above the mean. Learn about the statistical principle that the sum of deviations from the mean equals zero. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation