Question

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.

U:	6.0	5.0	11.0	33.0	4.0	5.0	80.0	18.0	35.0	17.0	23.0
F:	2.0	12.0	11.0	7.0	9.0	9.0	5.0	20.0	5.0	8.2	21.0	8.2	2.0	3.0	0.6

(a) Determine the sample mean for each sample. (Round your answers to two decimal places.)

urban homes	1 EU/mg
farm homes	2 EU/mg

How do they compare?

The average endotoxin concentration in farm homes is more than double the average concentration in urban homes. The average endotoxin concentration is about the same in both urban and farm homes.     The average endotoxin concentration in urban homes is more than double the average concentration in farm homes.

(b) Determine the sample median for each sample.

urban homes	4 EU/mg
farm homes	5 EU/mg

How do they compare?

1) The median endotoxin concentration is about the same in both urban and farm homes. 2)The median endotoxin concentration in farm homes is roughly double the median concentration in urban homes. 3) The median endotoxin concentration in urban homes is roughly double the median concentration in farm homes.

Why is the median for the urban sample so different from the mean for that sample?

1) The mean and median for urban homes are so different because the few large values raise the mean but not the median. 2) The mean and median for urban homes are so different because the measure different aspects of the distribution. 3) The mean and median for urban homes are so different because there are fewer observations.

(c) Calculate the trimmed mean for each sample by deleting the smallest and largest observation. (Round your answers to two decimal places.)

urban homes	8 EU/mg
farm homes	9 EU/mg

What are the corresponding trimming percentages? (Round your answers to two decimal places.)

urban homes	10 %
farm homes	11 %

How do the values of these trimmed means compare to the corresponding means and medians?
Urban homes:

The trimmed mean is 12    ---Select--    less thangreater thanequal to the mean of the entire sample. The trimmed mean is 13 ---Select--- less thangreater thanequal to the median of the entire sample.

Farm homes:

The trimmed mean is 14---Select---less thangreater thanequal to the mean of the entire sample. The trimmed mean is 15---Select---less thangreater thanequal to the median of the entire sample.

Answer 1

By using MINITAB,

Descriptive Statistics: U, F

Variable Mean TrMean Median
U 21.55 17.00 17.00
F 8.20 7.80 8.20

a] Mean

Urban Homes = 21.55 EU/Mg

Farm homes = 8.20 EU/Mg

The average endotoxin concentration in urban homes is more than double the average concentration in farm homes.

b] Median

Urban Homes = 17.00 EU/Mg

Farm homes = 8.20 EU/Mg

3) The median endotoxin concentration in urban homes is roughly double the median concentration in farm homes.

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

c] Trimmed mean

Urban Homes = 17.00 EU/Mg

Farm homes = 7.80 EU/Mg