25. A transformation of data values by means of some mathematical function, such as or 1/x, can often yield a set of numbers that has “nicer” statistical properties than the original data. In particular, it may be possible to find a function for which the histogram of transformed values is more symmetric (or, even better, more like a bell-shaped curve)

than the original data. As an example, the article “Time Lapse Cinematographic Analysis of Beryllium–Lung Fibroblast Interactions” (Environ. Research, 1983: 34–43)

reported the results of experiments designed to study the behavior of certain individual cells that had been exposed to beryllium. An important characteristic of such an individual cell is its interdivision time (IDT). IDTs were determined for a large number of cells, both in exposed 1x treatment) and unexposed (control) conditions. The authors of the article used a logarithmic transformation, that is, . Consider the following representative IDT data:
transformed value 5 log(original value IDT log10(IDT) IDT log10(IDT) IDT log10(IDT)
28.1 1.45 60.1 1.78 21.0 1.32 31.2 1.49 23.7 1.37 22.3 1.35 13.7 1.14 18.6 1.27 15.5 1.19 46.0 1.66 21.4 1.33 36.3 1.56 25.8 1.41 26.6 1.42 19.1 1.28 16.8 1.23 26.2 1.42 38.4 1.58 34.8 1.54 32.0 1.51 72.8 1.86 62.3 1.79 43.5 1.64 48.9 1.69 28.0 1.45 17.4 1.24 21.4 1.33 17.9 1.25 38.8 1.59 20.7 1.32 19.5 1.29 30.6 1.49 57.3 1.76 21.1 1.32 55.6 1.75 40.9 1.61 31.9 1.50 25.5 1.41 28.9 1.46 52.1 1.72 Use class intervals to construct a histogram of the original data. Use intervals to do the same for the transformed data. What is the effect of the transformation?