The mean of 19 observations is 4. If one more observation of 24 is added to the data, the new mean will be:

Options

A. 4
B. 5
C. 6
D. 7

Answer

To solve the problem step by step, we will follow these calculations:

1. **Understanding the Mean**:
The mean (average) is calculated as the sum of all observations divided by the number of observations.

2. **Calculating the Sum of the Initial Observations**:
We know that the mean of 19 observations is 4. Therefore, we can find the sum of these observations using the formula:
\[ \text{Sum} = \text{Mean} \times \text{Number of Observations} \]
Substituting the given values:
\[ \text{Sum} = 4 \times 19 = 76 \]

3. **Adding the New Observation**:
We are adding one more observation which is 24. We will add this to the sum we calculated:
\[ \text{New Sum} = 76 + 24 = 100 \]

4. **Calculating the New Number of Observations**:
The new number of observations will be the original 19 observations plus the new one:
\[ \text{New Number of Observations} = 19 + 1 = 20 \]

5. **Calculating the New Mean**:
Now we can calculate the new mean using the new sum and the new number of observations:
\[ \text{New Mean} = \frac{\text{New Sum}}{\text{New Number of Observations}} = \frac{100}{20} = 5 \]

Thus, the new mean after adding the observation of 24 is **5**.