The average of a collection of 20 measurements was calculated to be 56 cm . But later it was found that a mistake occurred in one of the measurements which recorded as 64 m but should have been 61 cm ? What is the correct average ?

Answer

To find the correct average after a mistake in one of the measurements, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- The average of the measurements is given as 56 cm.
- The total number of measurements is 20.
- The incorrect measurement is recorded as 64 cm, but it should have been 61 cm.

2. **Calculate the initial sum of the measurements:**
- The formula for average is:
\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Total observations}} \]
- Rearranging this gives us:
\[ \text{Sum of observations} = \text{Average} \times \text{Total observations} \]
- Substituting the known values:
\[ \text{Sum of observations} = 56 \, \text{cm} \times 20 = 1120 \, \text{cm} \]

3. **Adjust the sum for the correct measurement:**
- Since the incorrect measurement (64 cm) needs to be replaced with the correct measurement (61 cm), we need to adjust the sum:
\[ \text{New Sum} = \text{Old Sum} - \text{Incorrect Measurement} + \text{Correct Measurement} \]
- Substituting the values:
\[ \text{New Sum} = 1120 \, \text{cm} - 64 \, \text{cm} + 61 \, \text{cm} \]
- Calculating this gives:
\[ \text{New Sum} = 1120 - 64 + 61 = 1117 \, \text{cm} \]

4. **Calculate the new average:**
- Now, we can find the new average using the new sum:
\[ \text{New Average} = \frac{\text{New Sum}}{\text{Total observations}} = \frac{1117 \, \text{cm}}{20} \]
- Performing the division:
\[ \text{New Average} = 55.85 \, \text{cm} \]

### Final Answer:
The correct average is **55.85 cm**.

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