A medical researcher in India obtained blood specimens from 31 young children, all of whom were infected with malaria. The following data, listed in increasing order, are the numbers of malarial parasites found in 1 ml of blood from each child.

(a) Construct a frequency distribution of the data, using a class width of 10,000: display the distribution as a histogram.
(b) Transform the data by taking the logarithm (base 10) of each observation. Construct a frequency distribution of the transformed data and display it as a histogram. How does the log transformation affect the shape of the frequency distribution?
(c) Determine the mean of the original data and the mean of the log-transformed data. Is the mean of the logs equal to the log of the mean?
(d) Determine the median of the original data and the median of the log-transformed data. Is the median of the logs equal to the log of the median?

Transcribed Image Text:

100 140 140 27 400 435 455 770 826 1400 1,540 1,640 1.920 2.280 2340 3,672 914 6,160 6,560 6,741 7,609 8,547 9560 10,516 14,960 16,855 18,600 22,995 29,800 83.200 134,232