Question

2. The following data of the dust levels in both urban homes and farm homes is given below as:

U: 6.0, 5.0, 11.0, 33.0, 4.0, 5.0, 80.0, 18.0, 35.0, 17.0, 23.0

F: 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

a) Compute sample mean, median and quartiles of each sample. How do they compare? Comment on your findings.

b) Construct a stem-and-leaf diagram for each sample and a comparative box plot. Compare the two samples and comment on the possible presence of outliers.

Answer 1

2.)

for urban homes:

4
5
5
6
11
17
18
23
33
35
80

Mean=(4+5+5+6+11+17+18+23+33+35+80)/11=21.54545  

Median=data in the Middle =17

Lower Quartile(Q1)=Median of the Lower half of the data

Lower half=4,5,,5,6,11,17

Lower Quartile(Q1)=(5+6)/2=5.5

Upper Quartile(Q3)=Median of the Upper half of the data

Upper Half:17,18,23,33,35,80

Upper Quartile(Q3)=(23+33)/2=28

For farm homes

0.3
2
3
4
4
5
8
8.9
9
9
9.2
11
14
20
21

Mean=8.56

Median=8.9

Lower Quartile(Q1)=4

Upper Quartile(Q3)=10.1

From the above observations we can say the mean, median, upper quartile and lower quartile of the urban homes is greater

b.)

stem-and-leaf diagram for urban homes

stem-and-leaf diagram for farm homes

box plot for urban homes

from the box plot we can see there is one outlier (point:80)

box plot for farm homes

There is no outlier