The mean of a dataset is 27.8 and we add a new value 32.3. What will happen to Group of answer choicesCannot be determinedIncreasesWill remain the sameDeceases

Break Down the Problem

1. Identify the effect of adding a new value to the dataset on the mean.

Relevant Concepts

2. The mean is calculated by the formula: $\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$ When a new value is added, the formula will adjust because both the sum of values and the count of values will change.

Analysis and Detail

3. If the original mean is 27.8, it means: $\text{Sum of all values} = 27.8 \times n \quad \text{(where \( n \) is the number of values)}$ After adding a new value (32.3), the new mean will be: $\text{New Mean} = \frac{(27.8 \times n) + 32.3}{n + 1}$ We need to assess if this new mean would be greater than, less than, or equal to 27.8.

Verify and Summarize

4. Adding a value (32.3) that is greater than the current mean (27.8) will result in a new mean that is higher than the original mean.

Final Answer

The mean will increase.