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.
Col1 U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0
Col2 F: 2.0 15.0 12.0 8.0 8.0 7.0 6.0 19.0 3.0 9.8 22.0 9.6 2.0 2.0 0.5
(a) Determine the sample mean for each sample. (Round your answers to two decimal places.)(b) Determine the sample median for each sample.c) Calculate the trimmed mean for each sample by deleting the smallest and largest observation. (Round your answers to two decimal places.)d. What are the corresponding trimming percentages? (Round your answers to two decimal places.)

Answer 1

Answer:

a. sample mean for U is 21.55 and sample mean for F is 8.39

b. sample median for U is 17 and sample median for F is 8

c. trimmed mean for U is 17 and trimmed mean for F is 7.95

d. trimmed percentage for U is 18.18% and trimmed percentage for F is 13.33%

Step-by-step explanation:

a) Sample mean can be calculated by adding values and dividing the sum by the number of the values

$Mean(U)=\frac{6.0+5.0+11.0+33.0+4.0+5.0+80.0+18.0+35.0+17.0+23.0}{11}$ ≈ 21.55

$Mean(F)=\frac{2.0+15.0+12.0+8.0+8.0+7.0+6.0+19.0+3.0+9.8+22.0+9.6+2.0+2.0+0.5}{15}$ ≈ 8.39

b) Sample median is the middle value of a sorted sample:

Sorted(U)= [ 4.,  5.,  5.,  6., 11., 17., 18., 23., 33., 35., 80.]

Sorted(F)=[ 0.5,  2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. , 22.]

Median(U)=17, which is the 6.th (middle) value

Median(F)=8, which is the 8.th (middle) value

c) If we delete the the smallest and largest observation, we have:

U= [  5.,  5.,  6., 11., 17., 18., 23., 33., 35., ]

F= [ 2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. ]

Using the above equation for the new samples, we have:

TrimmedMean(U)= 17

TrimmedMean(F)=7.95

d) Trimming percentages can be found by dividing number of removed values by the old sample size

That is, for U:  $\frac{2}{11} =0.18$ , 18.18%

for F:  $\frac{2}{15} =0.13$ , 13.33%