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Q.

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 mm, 5.55 mm, 5.45 mm; 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as :

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a

$(5.5375 \pm 0.0740) m m$

b

$(5.538 \pm 0.074) m m$

c

$(5.5375 \pm 0.0739) m m$

d

$(5.54 \pm 0.07) m m$

answer is C.

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Detailed Solution

As significant figures in each measurement is 3, the diameter should be recorded in three significant figures.
$∴$ key is option (3).

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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 mm, 5.55 mm, 5.45 mm; 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as :