Mean of 11 observations is 17.5 . If one observation value 15 is deleted, then the mean of remaining observation is ________

Options

A. `15.75`
B. `16.75`
C. `17.75`
D. `18.75`

Answer

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

### Step 1: Calculate the sum of the original observations.
Given:
- Mean of 11 observations = 17.5
- Number of observations (n) = 11

Using the formula for mean:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
We can rearrange this to find the sum of observations:
\[ \text{Sum of observations} = \text{Mean} \times \text{Number of observations} \]
Substituting the known values:
\[ \text{Sum of observations} = 17.5 \times 11 = 192.5 \]

### Step 2: Calculate the new sum of observations after deleting one observation.
We need to delete the observation with the value of 15:
\[ \text{New sum of observations} = \text{Original sum} - \text{Deleted observation} \]
Substituting the values:
\[ \text{New sum of observations} = 192.5 - 15 = 177.5 \]

### Step 3: Calculate the new number of observations.
Since we deleted one observation from the original 11:
\[ \text{New number of observations} = 11 - 1 = 10 \]

### Step 4: Calculate the new mean.
Using the new sum and the new number of observations:
\[ \text{New Mean} = \frac{\text{New sum of observations}}{\text{New number of observations}} \]
Substituting the values:
\[ \text{New Mean} = \frac{177.5}{10} = 17.75 \]

### Final Answer:
The mean of the remaining observations is **17.75**.

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