Question:
R - charts are preferable over \(\sigma\) - charts because:
R - charts are preferable over \(\sigma\) - charts because:
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Check each stated reason separately for small samples, you will find all of them hold true.
Updated On: Jul 4, 2026
- Both of these fluctuate together in case of small samples
- R is easily calculated
- R charts are economical
- All of these
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The Correct Option is D
Solution and Explanation
Step 1: In statistical quality control, the range \(R\) (largest minus smallest observation in a sample) and the standard deviation \(\sigma\) both measure the spread of a sample and can be used to build a control chart.
Step 2: For small sample sizes, typically \(n \le 10\), the sampling distributions of \(R\) and \(\sigma\) are known to move together closely, so a chart based on \(R\) gives essentially the same quality control signal as one based on \(\sigma\).
Step 3: Computing \(R\) only requires finding the maximum and minimum of the sample and subtracting, which is far quicker than computing a standard deviation that needs squaring deviations, summing, dividing and taking a square root. This also makes it economical in time and effort on the shop floor, where charts are updated frequently by relatively less technically trained staff.
Step 4: Since all three properties described in the options, namely the two measures fluctuating together for small samples, easy calculation of \(R\), and the resulting economy of the R-chart, are valid reasons, the correct choice is All of these.
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