A student measuring the diameter of a pencil of circular cross-section

Question:

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings $5.50 \mathrm{~mm}, 5.55 \mathrm{~mm}, 5.45 \mathrm{~mm}$, $5.65 \mathrm{~mm}$, The average of these four reading is $5.5375 \mathrm{~mm}$ and the standard deviation of the data is $0.07395 \mathrm{~mm}$. The average diameter of the pencil should therefore be recorded as:

1. (1) $(5.5375 \pm 0.0739) \mathrm{mm}$

2. (2) $(5.5375 \pm 0.0740) \mathrm{mm}$

3. (3) $(5.538 \pm 0.074) \mathrm{mm}$

4. (4) $(5.54 \pm 0.07) \mathrm{mm}$

Correct Option: , 4

Solution:

(4) Average diameter, $d_{\mathrm{av}}=5.5375 \mathrm{~mm}$

Deviation of data, $\Delta d=0.07395 \mathrm{~mm}$

As the measured data are upto two digits after decimal, therefore answer should be in two digits after decimal.

$\therefore d=(5.54 \pm 0.07) \mathrm{mm}$