Answer to Question #240967 in Statistics and Probability for Mohammad Moqsien

Question

1.1 The following measurements were recorded for
the drying time, in hours, of a certain brand of latex
paint.
3.4 2.5 4.8 2.9 3.6
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
Assume that the measurements are a simple random
sample.
(a) What is the sample size for the above sample?
(b) Calculate the sample mean for these data.
(c) Calculate the sample median.
(d) Plot the data by way of a dot plot.
(e) Compute the 20% trimmed mean for the above
data set.
(f) Is the sample mean for these data more or less descriptive as a center of location than the trimmed
mean?

Answer 1

a) the size of sample is 15

b) sample mean is calculated as arithmetic mean of all it's elements. So, $m=57/15=3.8$

c) to define median we will sort the elements ascending, and pick the eight element as median: 2.5 2.8 2.8 2.9 3.0 3.3 3.4 3.6 ...

The median is 3.6

d) the plot is in attached photo

e) to compute 20% trmed mean we should delete from sample 20% of the largest and 20% of the smallest elements, and compute mean of the new sample.

New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8

$M2=33.3/9=3.7$

f) the mean is 3.8, the median is 3.6, the trimmed mean is 3.7. So, the sample mean is less descriptive as the centre of location(median) than the trimmed mean

Attached photo: