The mean of 20 numbers is 35. If four numbers 24, 20, 21 and 27 are removed, then what will be the mean of remaining numbers?

Options

A. a)38
B. b)40
C. c)33
D. d)37

Answer

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

### Step 1: Calculate the total sum of the original 20 numbers.
The mean of the 20 numbers is given as 35. The formula for the mean is:

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

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

\[ \text{Total Sum} = \text{Mean} \times \text{Number of Items} = 35 \times 20 = 700 \]

### Step 2: Calculate the sum of the numbers being removed.
The numbers being removed are 24, 20, 21, and 27. We need to find their total sum:

\[ \text{Sum of removed numbers} = 24 + 20 + 21 + 27 \]

Calculating this step by step:

\[ 24 + 20 = 44 \]
\[ 44 + 21 = 65 \]
\[ 65 + 27 = 92 \]

So, the sum of the removed numbers is 92.

### Step 3: Calculate the new total sum after removing the numbers.
Now, we subtract the sum of the removed numbers from the original total sum:

\[ \text{New Total Sum} = 700 - 92 = 608 \]

### Step 4: Calculate the number of remaining numbers.
Initially, there were 20 numbers, and we removed 4 numbers:

\[ \text{Remaining Numbers} = 20 - 4 = 16 \]

### Step 5: Calculate the new mean of the remaining numbers.
Now, we can find the new mean using the new total sum and the number of remaining numbers:

\[ \text{New Mean} = \frac{\text{New Total Sum}}{\text{Remaining Numbers}} = \frac{608}{16} \]

Calculating this gives:

\[ 608 \div 16 = 38 \]

Thus, the new mean of the remaining numbers is **38**.

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