1. Given data

The four measured diameters are: $5.50\ \text{mm},\ 5.55\ \text{mm},\ 5.45\ \text{mm},\ 5.65\ \text{mm}$

Given:

• Mean value = $\bar{x} = 5.5375\ \text{mm}$
• Standard deviation = $\sigma = 0.07395\ \text{mm}$

We must write the measured value in proper experimental form.

2. Rule for reporting experimental results

A measured quantity is usually reported as: $\text{measured value} = (\text{mean} \pm \text{uncertainty})$

with the following conventions:

• The uncertainty should usually be written with one significant figure (sometimes two if the first digit is 1 or 2, but here one significant figure is standard).
• The mean value should be rounded off to the same decimal place as the uncertainty.

3. Round the standard deviation

Given: $0.07395\ \text{mm}$

Rounded to one significant figure: $0.07\ \text{mm}$

4. Round the mean to the same decimal place

Since the uncertainty is $0.07\ \text{mm}$, it is correct up to the hundredths place. So the mean should also be written up to the hundredths place:

$5.5375\ \text{mm} \approx 5.54\ \text{mm}$

5. Final reported result

Therefore, the diameter should be recorded as: $\boxed{(5.54 \pm 0.07)\ \text{mm}}$

6. Check options

• A: $(5.54 \pm 0.07)\ \text{mm}$ ✅ Correct
• B: $(5.5375 \pm 0.0740)\ \text{mm}$ ❌ Too many digits retained
• C: $(5.5375 \pm 0.0739)\ \text{mm}$ ❌ Too many digits retained
• D: $(5.538 \pm 0.074)\ \text{mm}$ ❌ Still over-precise

Hence, the correct option is A.