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 $5.50\text{mm},$ $5.55\text{mm,}$$5.45\text{mm},5.65\text{mm}.$ The average of these four reading is $5.5375\text{mm}$ and the standard deviation of the data is $0.07395\text{mm}.$ The average diameter of the pencil should therefore be recorded as :

• A. $(5.5375\pm 0.0739)\text{mm}$
• B. $(5.5375\pm 0.0740)\text{mm}$
• C. $(5.538\pm 0.074)\text{mm}$
• D. $(5.54\pm 0.07)\text{mm}$

Answer 1

The correct option is D $(5.54\pm 0.07)\text{mm}$

Given:
Average diameter, $d_{av}=5.5375\text{mm}$
Deviation of data, $\Delta d=0.07395\text{mm}$

As the measured data are upto two digits after decimal, therefore answer should be in two digits after decimal. So we need to round off the given values in two digits after decimal.

$d_{av}=5.5375\text{mm}$
$\Rightarrow d_{av}=5.5400\text{mm}$

and
$\Delta d=0.07395\text{mm}$
$\Rightarrow \Delta d=0.07400\text{mm}$
$\Rightarrow \Delta d=0.07000\text{mm}$

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

Hence, option $\left(\text{D}\right)$ is correct.