The mean of 30 observations of a data was calculated 24.1. At a later stage, we noticed that a value 18.2 was wrongly read as 12.2. Find the value of the correct mean

Options

A. 23
B. 23.3
C. 24
D. 24.3

Answer

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

### Step 1: Calculate the Incorrect Sum of Observations
The mean of the 30 observations was calculated as 24.1. To find the sum of these observations, we use the formula:
\[ \text{Sum of Observations} = \text{Mean} \times \text{Number of Observations} \]
Substituting the given values:
\[ \text{Sum of Observations} = 24.1 \times 30 = 723 \]

### Step 2: Identify the Incorrect and Correct Observations
The incorrect observation was read as 12.2 instead of the correct value of 18.2.

### Step 3: Calculate the Correct Sum of Observations
To find the correct sum, we need to adjust the incorrect sum by removing the incorrect observation and adding the correct observation:
\[ \text{Correct Sum} = \text{Incorrect Sum} - \text{Incorrect Observation} + \text{Correct Observation} \]
Substituting the values:
\[ \text{Correct Sum} = 723 - 12.2 + 18.2 \]
Calculating this step by step:
1. \( 723 - 12.2 = 710.8 \)
2. \( 710.8 + 18.2 = 729 \)

### Step 4: Calculate the Correct Mean
Now that we have the correct sum, we can find the correct mean using the same formula:
\[ \text{Correct Mean} = \frac{\text{Correct Sum}}{\text{Number of Observations}} \]
Substituting the values:
\[ \text{Correct Mean} = \frac{729}{30} \]
Calculating this gives:
\[ \text{Correct Mean} = 24.3 \]

### Final Answer
The correct mean of the observations is **24.3**.

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