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
[tex]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}[/tex] ≈ 21.55
[tex]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}[/tex] ≈ 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: [tex]\frac{2}{11} =0.18[/tex] , 18.18%
for F: [tex]\frac{2}{15} =0.13[/tex] , 13.33%
