Average of 15 numbers is 20. If a number 4 is also included, then what will be the average of these 16 numbers

Options

A. 17
B. 18
C. `18.5`
D. 19

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Calculate the total sum of the 15 numbers.
Given that the average of 15 numbers is 20, we can use the formula for average:

\[ \text{Average} = \frac{\text{Total Sum}}{\text{Number of Items}} \]

So, we can rearrange this to find the total sum:

\[ \text{Total Sum} = \text{Average} \times \text{Number of Items} \]

Substituting the given values:

\[ \text{Total Sum} = 20 \times 15 = 300 \]

### Step 2: Add the new number to the total sum.
Now, we need to include the new number, which is 4, to the total sum we calculated:

\[ \text{New Total Sum} = 300 + 4 = 304 \]

### Step 3: Calculate the new average.
Now that we have the new total sum and the new number of items (which is 16), we can calculate the new average:

\[ \text{New Average} = \frac{\text{New Total Sum}}{\text{New Number of Items}} = \frac{304}{16} \]

### Step 4: Simplify the fraction.
To simplify \( \frac{304}{16} \):

\[ \frac{304}{16} = 19 \]

### Conclusion:
Thus, the average of these 16 numbers is **19**.

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