Suppose that Rita and Rony both measure the lengths of four plants as part of an experiment. Rita measures in centimetres(cm) and her data are 1.5, 2.0, 2.7 and 1.8 cms while Rony measures the same plants in millimetres (mm). Rony’s data are 15, 20, 27 and 18.

Rita calculated the standard deviation for the data as 0.59 cm. What would be the corresponding value for Rony’s data?

Question

Suppose that Rita and Rony both measure the lengths of four plants as part of an experiment. Rita measures  in centimetres(cm) and her data are 1.5, 2.0, 2.7 and 1.8 cms while Rony measures the same plants in millimetres (mm). Rony’s data are 15, 20, 27 and 18.

Rita calculated the standard deviation for the data as 0.59 cm. What would be the corresponding value for Rony’s data?

BlackTom AI · Accepted Answer

We start by restating the information: Rita’s data are in centimetres (cm) and have a reported standard deviation of 0.59 cm. Rony’s measurements are the same lengths but in millimetres (mm). To compare standard deviations across units, we convert the unit of measurement for Rony’s data to the same unit as Rita’s, or convert Rita’s SD to millimetres.

Key idea: 1 cm equals 10 mm, so standard deviation scales by the same factor when units are converted. Therefore, if Rita’s SD is 0.59 cm, the corresponding SD for the same data expressed in millimetres is 0.59 × 10 = 5.9 mm.

Now evaluate each option:
Option 1: 5.1 mm. This would correspond to a 0.51 cm SD if you divided by 10, which does not match the given 0.59 cm for Rita, nor the correct conversion of 0.59 cm to millimetres (which should be 5.9 mm). Thus this option is incorrect.
Option 2: 5.1 cm. This is an incorrect unit; it would be 51 mm, which is far from the correctly converted 5.9 mm. The number also mismatches the expected magnitude after unit conversion, so it is wrong.
Option 3: 26 cm. This is orders of magnitude larger and clearly inconsistent with the data scale and the conversion rule. It is incorrect.
Option 4: 26 mm. This is again far larger than the properly converted 5.9 mm and does not respect the linear scaling from cm to mm. It is incorrect.

Summary: The correct conceptual approach is to convert Rita’s standard deviation to millimetres by multiplying by 10, yielding 5.9 mm. Among the given options, none matches 5.9 mm exactly, and the remaining choices either have incorrect units or implausibly large magnitudes. The closest numerical value in the list is 5.1 mm, but it is still not correct. The discrepancy highlights a mismatch between the provided SD (0.59 cm) and the options supplied.

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