Analysis and Improvement of Statistical Data and Graphs

This assignment involves analyzing and improving statistical data and graphs. It includes identifying issues with scaling and formatting, providing recommendations for improvement, and explaining how to create informative axes and visualizations. The assignment also discusses the importance of considering sample bias and recommends taking surveys from various sources. Specific details are provided for each section, including the analysis of a tree diagram, the calculation of probabilities, and the explanation of graph improvements.

STATISTICS

TABLE OF CONTENTS
QUESTION 1...................................................................................................................................3
a. Classification of variable.........................................................................................................3
b. Calculate..................................................................................................................................3
c. 85 Percentile............................................................................................................................4
d. Graph of satisfaction level......................................................................................................4
e. Mean would be an appropriate measure of central location or not.........................................4
f. Drafting graph for suggesting presence of association among various variables....................5
g. Answering through pivot table................................................................................................5
h. Relationship between employee left and performance evaluation..........................................6
I. Suitability of graph for two numerical variable.......................................................................6
2...................................................................................................................................................6
2.a Tree Diagram.........................................................................................................................6
(b)................................................................................................................................................6
(c)................................................................................................................................................7
(d) Recommendations.................................................................................................................7
3. Briefly explaining graph about ways which could be improved.............................................7
3.a ...............................................................................................................................................7
3.b ...............................................................................................................................................8
3.c................................................................................................................................................8
4. Indicating that outcome would be biased or not.....................................................................9

QUESTION 1
a. Classification of variable
Variable Classification
Satisfaction level Ordinal variable
last_evaluation Ordinal variable
number_project Nominal variables
average_monthly_hours Continuous variable
time_spend_company Numeric variables
work_accident Nominal variables
left Nominal variables
promotion_last_5 years Nominal variables
department Discrete variables
salary Ordinal variable
b. Calculate
average_monthly_hours
Mean 201.035016341
Standard Error 0.407587886
Median 200
Mode 135
Standard Deviation 49.9074681515
Sample Variance 2490.755377296
Kurtosis -1.1372249186
Skewness 0.0522986033
Range 214

Minimum 96
Maximum 310
Sum 3014118
Count 14993
Quartile 1 156
Quartile 3 245
IQR 89
c. 85 Percentile
85/100 0.85
0.85*14993 12744.05
12744.05+0.5 12744.55
12744th + 12755 260 + 260
(1-decimal)*12744th+0.5*12745 260
d. Graph of satisfaction level
0.09-0.19
0.29-0.39
0.49-0.59
0.69-0.79
0.89-0.99
0
500
1000
1500
2000
2500
C o u n t o f s a ti s f a c ti o n _le v e l
C ount of s a ti s fa cti on_le v e l

e. Mean would be an appropriate measure of central location or not
The mean would be not considered as appropriate measure of level of satisfaction as it is
not reflecting histogram of age wise employees level of satisfaction. If it would be placing
category as age wise then its mean would be considering various factors for level of satisfaction.
f. Drafting graph for suggesting presence of association among various variables
g. Answering through pivot table
Left
Yes No
marketing 5.70% 5.70%
IT 7.70% 8.30%
sales 28.40% 27.30%
support 15.60% 14.70%
technical 19.50% 17.70%
accounting 5.70% 4.90%
management 2.60% 4.70%
hr 6.00% 4.60%
product_mng 5.60% 6.20%
RandD 3.40% 5.80%

h. Relationship between employee left and performance evaluation
I. Suitability of graph for two numerical variable
In the context of suitability of graph for two variable must consider them at similar time.
There relation should be justified algebraically by both function or equation of variables. Its
major application to reflect relationship of two dimensional graphs. These type of graph is
known as scatter diagram and very useful device due to simple relationship among specified
variables and it could be observed easily if data is plotted easily.
2.
2.a Tree Diagram
(a) LAT +ve 0.89
Positive LAT -ve 0.11
HI Result
Negative LAT +ve 0.02
LAT -ve 0.98
(b)
1 P(HI positive) 0.89
2 P(LAT -ve ^ HI Negative)
P(LAT -ve) * P(HI
negative)
0.4802

3 P(LAT – ve
4 P(LAT +ve) 1
5 P(LAT -ve) 0.003
(c)
If variables are mutually exclusive then its sum should be equal to one. But in this
scenario. Probability of HI positive and LAT positive is equal to 1.89. Hence, it is considered as
independent variable.
P(HI positive) 0.89
LAT(Positive) 1
(d) Recommendations
The probability of LAT test is higher than HI gold standard, then on this basis it is
recommended that LAT test is more replicated from HI gold standard.
3. Briefly explaining graph about ways which could be improved
3.a
The above graph is depicting total world population but there is mistake in scaling and
appropriate formatting. There is presence of credibility along with proper display of name with
respect to data. The axes should be informative by considering value of data point at largest
scenario. The below table is depicting difference between scaling and for improving it should be
scaled equally along with perfect distribution of time.
Amount 1 Amount 2 Scaling difference
3000000 10000 2990000

300000000 3000000 297000000
1000000000 300000000 700000000
7000000000 1000000000 6000000000
7000000000
3.b
The above picture is not replicating format of graph in appropriate format. There should
be presence of data variation instead of design variation. It should provide identification in
appropriate elements along with specific proportion for the quantities which is presented in
numerical format. It must use bar or column chart with proper scaling of height in meter.

3.c
The above graph is not replicating proper scenario. It should be improved by providing
information on both axis as its data set is in continuous format. It should use proper scaling along
with visualized based on trend with specific time period along with data points which is very
high.
4. Indicating that outcome would be biased or not
Every survey should consider sample as whole universe because it would be providing
outcome in justified and true aspect. It is considering population only of readers of New Zealand
Magazines and it s not tech savvy so in turn it would be time consuming. The scenario would be
providing bias outcome. It should take survey from various sources not only from one source
such as readers of Magazine.