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The average of 9 numbers is 19. If the average of the first four numbers is 14, then the average of the last 5 numbers is:
The formula for the average (arithmetic mean) of $$n$$ numbers is
$$\text{Average} = \frac{\text{Sum of the numbers}}{n}$$
Step 1: Find the total sum of all 9 numbers.
Given average of 9 numbers = $$19$$, so using the formula:
$$\text{Sum of 9 numbers} = 19 \times 9 = 171$$
Step 2: Find the sum of the first 4 numbers.
Given average of the first 4 numbers = $$14$$, hence:
$$\text{Sum of first 4 numbers} = 14 \times 4 = 56$$
Step 3: Find the sum of the last 5 numbers.
Total sum of all 9 numbers − sum of first 4 numbers:
$$\text{Sum of last 5 numbers} = 171 - 56 = 115$$
Step 4: Compute the average of the last 5 numbers.
Number of terms = $$5$$, therefore:
$$\text{Average of last 5 numbers} = \frac{115}{5} = 23$$
Hence, the required average is $$23$$.
Option D which is: 23
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