Mean of 20 observations is 15.5. Later on it was found that the observation 24 was taken as 42. The correct mean is-

Options

A. 14
B. 14.2
C. 14.4
D. 14.6

Answer

To find the correct mean after identifying the error in the observations, we can follow these steps:

### Step 1: Calculate the total sum of the original observations
Given that the mean of 20 observations is 15.5, we can calculate the total sum of these observations using the formula for mean:

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

So, we can rearrange this to find the sum:

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

Substituting the known values:

\[ \text{Sum of observations} = 15.5 \times 20 = 310 \]

### Step 2: Adjust the sum for the incorrect observation
The incorrect observation was recorded as 42 instead of the correct value of 24. To find the correct sum, we need to subtract the incorrect observation and add the correct one:

\[ \text{Correct Sum} = \text{Original Sum} - \text{Incorrect Observation} + \text{Correct Observation} \]

Substituting the values:

\[ \text{Correct Sum} = 310 - 42 + 24 \]

Calculating this:

\[ \text{Correct Sum} = 310 - 42 + 24 = 310 - 18 = 292 \]

### Step 3: Calculate the correct mean
Now that we have the correct sum of the observations, we can find the correct mean by dividing the correct sum by the number of observations:

\[ \text{Correct Mean} = \frac{\text{Correct Sum}}{\text{Number of observations}} = \frac{292}{20} \]

Calculating this gives:

\[ \text{Correct Mean} = 14.6 \]

### Final Answer
The correct mean of the observations is **14.6**.

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