Exposure to microbial products especially endotoxin may have

Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The following are data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes. Determine the sample mean for each sample. (Round your answers to two decimal places.) Urban homes EU/mg farm homes EU/mg How do they compare? Determine the sample median for each sample. Urban homes EU/mg farm homes EU/mg How do they compare? Why is the median for the urban sample so different from the mean for that sample? Calculate the trimmed mean for each sample by deleting the smallest and largest observation. (Round your answers to two decimal places.) urban homes EU/mg farm homes EU/mg What are the corresponding trimming percentages? (Round your answers to two decimal places.) urban homes % farm homes % How do the values of these trimmed means compare to the corresponding means and medians? Urban homes: The trimmed mean is the mean of the entire sample. The trimmed mean is the median of the entire sample. Farm homes: The trimmed mean is the mean of the entire sample. The trimmed mean is the median of the entire sample.

Solution

1) Sample mean urban homes = 21.545 = 21.55 (after rounding off to two decimals)

Farm homes = 8.11

Hence urban homes avg > double of farm homes

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2) Sample median urban homes = 17

Farm homes = 8

urban home median >double farm home median by 1

So first option

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The mean and median for urban homes are so different because the few large values raise the mean but not the median.

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Urban homes -17 (deleted 80 and 4)

farm homes (7.5) (Deleted ones are 0.1 and 24)

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