The mean of five scores is 37.A sixth score of 43 is added.What is the new mean?

1. Break Down the Problem

To find the new mean after adding a sixth score, we need to:

1. Calculate the total of the five scores based on the given mean.
2. Add the sixth score to this total.
3. Divide this new total by the new number of scores (which is 6).

2. Relevant Concepts

The mean (average) is calculated using the formula: $\text{Mean} = \frac{\text{Total of scores}}{\text{Number of scores}}$

3. Analysis and Detail

1. Calculate the total of the original five scores: Since the mean is 37 for five scores, we can find the total: $\text{Total of five scores} = \text{Mean} \times \text{Number of scores} = 37 \times 5 = 185$

2. Add the sixth score to this total: $\text{New total} = 185 + 43 = 228$

3. Calculate the new mean: $\text{New Mean} = \frac{\text{New total}}{\text{New number of scores}} = \frac{228}{6} = 38$

4. Verify and Summarize

We verified that the calculations were stepwise:

• Original total calculated correctly.
• Sixth score added accurately.
• New mean calculated using the new total and the new count of scores.

Final Answer

The new mean after adding the sixth score is $\boxed{38}$.