Radhika ,Supriya and Hema were asked to find the mass of a metal piece independently one by one using the same balance and same weight box. Each student was asked to take three observations. The students reported their result as shown in the following table:
Students Result reported Average
I II III
Radikha 1.325 1.326 1.325 1.325
Supriya 1.310 1.311 1.321 1.314
Hema 1.31 1.30 1.31 1.31
If the actual mass of the metal piece is 1.325g and the permitted uncertainty in the measurement is 0.001g, answer the following questions:
(i) Whose measurement is both accurate and precise? Justify your answer.
(ii) Whose measurement is precise and not accurate Justify your answer?
(iii) Whose measurements are neither accurate nor precise? Justify your answer

a) Radikha

b) Hema

c) Supriya

Explanation:

PRECISION measures the difference or closeness of two or more observed values while ACCURACY measures the difference between the sets of observations to a standard or a given value.

If the measured observation(s) are close to the standard value, then we say that the observations are accurate.

If the values within the ranges of observations are close, then we say the values are precise.

Given the reported value of masses of metal piece as measured by the students:

Result reported Average

Radikha 1.325, 1.326, 1.325, 1.325

Supriya 1.310, 1.311, 1.321, 1.314

Hema 1.31, 1.30, 1.31, 1.31

Actual mass of metal piece = 1.325g

Permitted uncertainty in measurement = 0.001g

a) Based on the observations compared to the standard value, it is seen that Rhadikha measurement is ACCURATE AND PRECISE. It is accurate because each of her observation are all close to the actual mass of the metal piece which is 1.325g, the only value that differs (1.326) vary with just 0.001g which is within the permitted uncertainty in measurement.

Her measurement is also PRECISE because the difference in the values of all observations are also within the permitted uncertainty in measurement which is 0.001g

b) Hema observations is NOT ACCURATE but it is PRECISE. The values are not accurate because the measured observations are not close to the actual mass of the metal based on the permitted uncertainty in measurement.

The values are precise though because the difference in the observations are close and are almost the same.

c) Supriya observations are not accurate and not precise. This is because the measured observations are not close to the actual mass of the metal and the difference in the observations values are not within the permitted uncertainty in measurement.

For example 1.321 - 1.311 = 0.010g which is more than 0.001g.

option number c is the right answer.