Class
Frequency
X
m
X
m
2
f · X
m
2
f· X
m
0199
12
99.5
9900.25
118803
1194
200399
12
299.5
89700.25
1076403
3594
400599
7
499.5
249500.25
1746502
3496.5
600799
1
699.5
489300.25
489300.3
699.5
800999
1
899.5
809100.25
809100.3
899.5
10001199
4
1099.5
1208900.25
4835601
4398
12001399
1
1299.5
1688700.25
1688700
1299.5
14001599
2
1499.5
2248500.25
4497001
2999
Total
40
6396
6793602
15261410
18580
S
=
√
n
(
∑ f· X
m
2
)
−(
∑f· X
m
)
2
n
(
n
−
1
)
S
=
√
40
(
15261410
)−(
18580
)
2
40
(
40
−
1
)
=
412.342
E) Compare step (
C
) and (
D
):
Although both steps were applied on the same data, we see a
significant difference between them.
Step C (
Original Data
)
Step D (
Grouped
Frequency Data
)
Mean
348.9189
502
Mode/Modal Class
500
Class (0199) and (200399)
Standard Deviation
295.9162
412.342
The main cause of this difference is because of the outliers that
exist in the second data set (Frequency distribution).
When it
comes to the mean
, we can see how the outliers really affected
it in the grouped frequency data and overestimated it. The
mean in step C was reasonable. The mode
was more accurate in
step C than step D since it was take from the original data. The
standard deviation
in step D is more varied than step C due to
the outliers.
F) Summary:
In this phase, we calculated the fivenumber summary to find
the theoretical upper and lower limit which guided us to find
the outliers and removing them for more accuracy. Then, a box
plot was constructed to show the data distribution and
skewness. We also calculated the mean, median, midrange and
standard deviation for the original data set (Expense). After that
we found the mean, modal class and standard deviation for the
same data but they were arranged in a frequency distribution
table rather than dealing with each data individually, without
removing the outliers. A comparison was made between step C
and D and the difference was obvious due to the effect of
outliers.
Bibliography:
Statistical Language
. (2013, June 18). Retrieved May 9, 2014, from Australian Bureau of Statitics:

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 Spring '10
 jhajiten
 Statistics, Standard Deviation, Frequency distribution, Project, Statistics