AP Statistics 1.7.C Unit Changes in Summary Statistics

Practise transforming means, medians, ranges, IQRs, standard deviations, variances, z-scores, and interval endpoints when measurement units change.

Exam points

For Y=aX+b, transform location by a and b, but scale SD, IQR and range only by |a|.
Scale variance by a^2 and recognise that positive linear unit changes leave z-scores unchanged.
Apply an inverse transformation to convert interval endpoints back to the original measurement units.

[Maximum number: 1]

The kelvin is a unit of measurement for temperature; 0 K is absolute zero, the temperature at which all thermal motion ceases. Conversion from Fahrenheit to Kelvin is given by $\mathrm{K}=\frac{5}{9} \times(\mathrm{F}-32)+273$ . The average daily temperature in Monrovia, Liberia, is 78.35°F with a standard deviation of 6.3°F. If a scientist converts Monrovia daily temperatures to the Kelvin scale, what will be the new mean and standard deviation?

Mean, 231.75 K; standard deviation, 3.5 K

Mean, 298.75 K; standard deviation, 3.5 K

Mean, 298.75 K; standard deviation, 258.72 K

Mean, 298.75 K; standard deviation, 276.5 K

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1.7.C—Calculate different units of measurement for summary statistics question 1