Answer:
a).
mean(U) = 21.54545
mean(F) = 8.56
Compare:
The mean of U is higher (as expected) compare to the mean of F.
b).
Median(U) = 17
Median(F) = 8.9
The median of U is higher (as expected) compare to the mean of F.
b ii). The median is not affected by outliers. There is evidence of outlier(s) in the data sets (see attached diagram). This is one of the possible reason why median could be less than the mean. Hence, the median of the Urban sample is different from the mean of the Urban sample because the is possible outliers in the data set.
c).
Trimmed mean of U = 16.14286
Trimmed mean of F = 7.566667
The corresponding trimmed mean percentages = 20%.
d).
The trimmed mean is smaller compare to the mean obtained directly from the data sets. It is also smaller to the median (though close to the median than the initial mean).
Step-by-step explanation:
By mean, we mean the sum of all observation divided by the number of observations or sample size (n).
By median, we mean the middle value when the data set/observations is sorted in ascending or descending order.
For replication, kindly use the R codes below:
U = c(6.0, 5.0, 11.0 ,33.0, 4.0, 5.0, 80.0, 18.0, 35.0, 17.0, 23.0)
F = c(4.0, 14.0, 11.0, 9.0, 9.0, 8.0, 4.0, 20.0, 5.0, 8.9, 21.0, 9.2, 3.0, 2.0, 0.3)
mean(U)
mean(F)
median(U)
median(F)
mean(U, trim = 0.2)
mean(F, trim = 0.2)
