Question
Download Solution PDFAn instrument is used to measure a quantity at different time instances, and the expected values of the quantity are to be the same; however, the measured values are different. A set of 5 measurements that were recorded at different time instances are 98, 101, 99, 100 and 102. Find the precision of the third measurement.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Precision: A measurement of consistency or repeatability of measurement i.e., successive reading does not differ.
The average of the measured value is given by,
\(\overline {{X_n}} = \sum \frac{{{X_n}}}{n}\)
Where Xn is the recorded readings, n is no. of recorded readings.
Precision for particular reading is given by,
Precision \( = 1 - \left| {\frac{{Respective\;Reading - \overline {{X_n}} }}{{\overline {{X_n}} }}} \right|\)
Calculation:
The average measurement value
\(\overline {{X_n}} = \frac{{98 + 101 + 99 + 100 + 102}}{5}\)
\(= \frac{{500}}{5} = 100\)
Given third measurement reading = 99
The 3rd reading precision is given as
\(= 1 - \left| {\frac{{99 - 100}}{{100}}} \right|\)
\( = 1 - \frac{1}{{100}} = 0.99\)
Last updated on May 29, 2025
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