Mean of 20 observations is 17. If observation 40 is replaced by 12, then the new mean is

Options

A. 15
B. 15.6
C. 16
D. None of these

Answer

To find the new mean after replacing one observation, we can follow these steps:

### Step 1: Calculate the sum of the original observations
The mean of the original 20 observations is given as 17. The formula for mean is:

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

We can rearrange this formula to find the sum of the observations:

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

Substituting the known values:

\[ \text{Sum of observations} = 17 \times 20 = 340 \]

### Step 2: Replace the observation
We need to replace the observation 40 with 12. To find the new sum of observations after this replacement, we subtract 40 from the original sum and add 12:

\[ \text{New Sum} = \text{Original Sum} - 40 + 12 \]

Calculating this gives:

\[ \text{New Sum} = 340 - 40 + 12 = 312 \]

### Step 3: Calculate the new mean
Now that we have the new sum of observations, we can calculate the new mean using the same mean formula. The number of observations remains 20, so:

\[ \text{New Mean} = \frac{\text{New Sum}}{\text{Number of observations}} = \frac{312}{20} \]

Calculating this gives:

\[ \text{New Mean} = 15.6 \]

### Final Answer
The new mean after replacing observation 40 with 12 is **15.6**.

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