The average of 10 numbers is 9.5. If a number 5 is removed, then what will be the new average?

Options

A. `9.75`
B. 10
C. `10.25`
D. 9

Answer

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

### Step 1: Calculate the total sum of the 10 numbers.
The average of 10 numbers is given as 9.5. The formula for average is:

\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of observations}} \]

So, we can rearrange this to find the sum:

\[ \text{Sum of numbers} = \text{Average} \times \text{Number of observations} \]

Substituting the values:

\[ \text{Sum} = 9.5 \times 10 = 95 \]

### Step 2: Remove the number 5 from the sum.
Now, we need to find the new sum after removing the number 5:

\[ \text{New Sum} = \text{Old Sum} - 5 = 95 - 5 = 90 \]

### Step 3: Calculate the new average.
After removing one number, we are left with 9 numbers. We can now calculate the new average:

\[ \text{New Average} = \frac{\text{New Sum}}{\text{Number of remaining observations}} = \frac{90}{9} \]

Calculating this gives:

\[ \text{New Average} = 10 \]

### Final Answer:
The new average after removing the number 5 is **10**.

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