Worksheet No.2/July- 2011

Part A: ACCURACY and PRECISION

Least Count:

The least count of an instrument is the smallest amount it is capable of measuring. For example, the least count of a metre scale is 1 mm.

We have 10 divisions between 0 to 1 so we can say that the least count is 1/ 10 or 0.1cm or 1mm.

Accuracy:

Accuracy refers to the closeness of the measured value to the true value. For example, if the true value of the length of a block is 20.6 cm and the value measured with a metre scale A is 20.4 cm whereas the value measured by metre scale B is 20.5 cm, then we say that the accuracy of the reading made with metre scale B is more than that made with metre scale A.

Is least count the same as accuracy? Discuss

Precision of measurements and of the instrument:

Let us consider two vernier calipers A and B, which are used to measure the length of a block. Let the true length of the block be 3.459 cm. The calipers are used to take five readings of the length of this block and the results are as follows:

Which calipers result is more precise (consistent) set of readings? ................

Now compare the readings taken with a meter scale (LC = 0.1 cm), vernier calipers (LC = 0.01 cm) and a screw gauge (LC = 0.001 cm)

Fill in the blanks:

The readings with each instrument are quite consistent (..).

In addition, the screw gauge has the smallest and hence the best...

[screw gauge; precise; least count; precision; accuracy; vernier calipers; meter scale; size]

True value = 3.459 cm

Precision thus refers to two things:

1. The closeness of measured values to each other (consistency of measured values). 2. The least count of the instrument. Smaller the least count, the more precise is the instrument. Accuracy and precision understood usinq the dart-board illustration:

The clustering of darts together represent 'precision' while the tendency of the darts to fall near or around the 'bull's eye' represents 'accuracy'.

Write the correct diagram alphabet next to each case shown:

Most accurate and least precise

Most accurate and precise

Least accurate but quite precise

Neither accurate nor precise

Table of comparison of accuracy and precision:

ACCURACY PRECISION

Accuracy expresses the closeness of the measurement to the true value.

Accuracy can be improved by recalibration of the instrument or by reducing human errors.

Precision of a set of measurements expresses the 'closeness' of the measurements to each other.

Precision of an instrument indicates the least count of the instrument.

Precision of an instrument cannot be improved as it is inherent in the instrument.

(a) (b) (c) (d)