In an experiment refractive index of glass was observed to be 1.45, 1.56, 1.54, 1.44, 1.54 and 1.53. The mean absolute error in the experiement is

Options

A. `+-0.04`
B. `0.02`
C. `-0.03`
D. `+-0.01`

Answer

To calculate the mean absolute error in the experiment, we will follow these steps:

### Step 1: Identify the Observed Values
The observed values of the refractive index of glass are:
- 1.45
- 1.56
- 1.54
- 1.44
- 1.54
- 1.53

### Step 2: Determine the Standard Value
In the transcript, it is mentioned that the standard value (or true value) for the refractive index is 1.51.

### Step 3: Calculate the Absolute Errors
We will calculate the absolute error for each observed value using the formula:
\[ \text{Absolute Error} = |\text{Observed Value} - \text{Standard Value}| \]

1. For 1.45:
\[ |1.45 - 1.51| = 0.06 \]

2. For 1.56:
\[ |1.56 - 1.51| = 0.05 \]

3. For 1.54:
\[ |1.54 - 1.51| = 0.03 \]

4. For 1.44:
\[ |1.44 - 1.51| = 0.07 \]

5. For 1.54:
\[ |1.54 - 1.51| = 0.03 \]

6. For 1.53:
\[ |1.53 - 1.51| = 0.02 \]

### Step 4: Sum the Absolute Errors
Now, we will sum all the absolute errors calculated:
\[ 0.06 + 0.05 + 0.03 + 0.07 + 0.03 + 0.02 = 0.26 \]

### Step 5: Calculate the Mean Absolute Error
To find the mean absolute error, we divide the total absolute error by the number of observations (which is 6):
\[ \text{Mean Absolute Error} = \frac{0.26}{6} \approx 0.0433 \]

### Step 6: Round the Result
Finally, we round the result to three significant figures:
\[ \text{Mean Absolute Error} \approx 0.04 \]

### Final Answer
The mean absolute error in the experiment is **0.04**.

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