To determine the effect of adding 10 points to one of the scores on the sample mean, follow these steps:

1. **Identify the original mean and the number of scores in the sample:**
- Mean (M) = 40
- Let the number of scores be $ n $.

2. **Calculate the total sum of the original scores:**
- Total sum of scores = $ M \times n = 40n $.

3. **Add 10 points to one of the scores:**
- New total sum of scores = $ 40n + 10 $.

4. **Calculate the new mean:**
- New mean = $ \frac{40n + 10}{n} $.

5. **Simplify the expression for the new mean:**
- New mean = $ 40 + \frac{10}{n} $.

Since $ \frac{10}{n} $ is a positive value, the new mean will be greater than the original mean of 40. Therefore, the sample mean increases.

Question

To determine the effect of adding 10 points to one of the scores on the sample mean, follow these steps:

1. **Identify the original mean and the number of scores in the sample:**
   - Mean (M) = 40
   - Let the number of scores be $ n $.

2. **Calculate the total sum of the original scores:**
   - Total sum of scores = $ M \times n = 40n $.

3. **Add 10 points to one of the scores:**
   - New total sum of scores = $ 40n + 10 $.

4. **Calculate the new mean:**
   - New mean = $ \frac{40n + 10}{n} $.

5. **Simplify the expression for the new mean:**
   - New mean = $ 40 + \frac{10}{n} $.

Since $ \frac{10}{n} $ is a positive value, the new mean will be greater than the original mean of 40. Therefore, the sample mean increases.

Knowee AI · Accepted Answer

To determine the effect of adding 10 points to one of the scores on the sample mean, follow these steps:

1. **Identify the original mean and the number of scores in the sample:**
   - Mean (M) = 40
   - Let the number of scores be $ n $.

2. **Calculate the total sum of the original scores:**
   - Total sum of scores = $ M \times n = 40n $.

3. **Add 10 points to one of the scores:**
   - New total sum of scores = $ 40n + 10 $.

4. **Calculate the new mean:**
   - New mean = $ \frac{40n + 10}{n} $.

5. **Simplify the expression for the new mean:**
   - New mean = $ 40 + \frac{10}{n} $.

Since $ \frac{10}{n} $ is a positive value, the new mean will be greater than the original mean of 40. Therefore, the sample mean increases.

A sample has a mean of M = 40. If 10 points are added to one of the scores, what happens to the sample mean?Group of answer choicesit decreases substantiallyit is unchangedit decreases a littleit increases