Understanding the Current Mean
To begin with, the mean of 19 observations is given as 24. The formula for calculating the mean is:
Mean = (Sum of Observations) / (Number of Observations)
Given that:
- Mean = 24
- Number of Observations = 19
We can find the total sum of these observations:
- Sum of Observations = Mean × Number of Observations
- Sum of Observations = 24 × 19 = 456
Adding a New Observation
Now, when we add one more observation of 24 to the existing data, the new number of observations becomes:
- New Number of Observations = 19 + 1 = 20
The new sum of observations now includes the additional observation:
- New Sum of Observations = Old Sum + New Observation
- New Sum of Observations = 456 + 24 = 480
Calculating the New Mean
To calculate the new mean with the updated sum and number of observations, we use the same mean formula:
- New Mean = (New Sum of Observations) / (New Number of Observations)
- New Mean = 480 / 20 = 24
Conclusion
The new mean remains the same at 24, despite the addition of another observation of 24. This illustrates that adding a value equal to the current mean does not change the overall mean.
- Key Takeaway: Adding a value equal to the mean does not affect the overall mean.