The average height of 30 boys was calculated to be 150 cm. it was detected later that one value of 165 cm was wrongly copied as 135 cm for the computations of the mean. Find the correct mean.

Answer

To find the correct mean height of the 30 boys after correcting the error in the recorded height, we can follow these steps:

### Step 1: Calculate the total height based on the given average.
The average height of the boys is given as 150 cm. The formula for the mean (average) is:

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

Given that the average height is 150 cm for 30 boys, we can calculate the total height:

\[ \text{Total Sum of Heights} = \text{Mean} \times \text{Number of Boys} = 150 \, \text{cm} \times 30 = 4500 \, \text{cm} \]

### Step 2: Identify the error in the recorded height.
It was detected that one height of 165 cm was wrongly recorded as 135 cm. We need to correct this error.

### Step 3: Calculate the difference caused by the error.
The difference between the correct height and the wrong height is:

\[ \text{Difference} = 165 \, \text{cm} - 135 \, \text{cm} = 30 \, \text{cm} \]

### Step 4: Adjust the total height to account for the error.
To find the correct total height, we need to add the difference to the previously calculated total height:

\[ \text{Correct Total Height} = 4500 \, \text{cm} + 30 \, \text{cm} = 4530 \, \text{cm} \]

### Step 5: Calculate the correct mean.
Now we can find the correct mean using the corrected total height:

\[ \text{Correct Mean} = \frac{\text{Correct Total Height}}{\text{Number of Boys}} = \frac{4530 \, \text{cm}}{30} = 151 \, \text{cm} \]

### Conclusion
The correct mean height of the 30 boys is **151 cm**.

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