Download Christian Rizzo App of Research in IT Descriptive Statistics with

Christian Rizzo
App of Research in IT
Descriptive Statistics with Three Variables
The statistics being analyzed are data received from multiple companies who are the
victims of DDoS attacks. The data that has been received displays each company that had DDoS
attacks, the amount of those attacks, the amount of protected devices within the company, and
which companies servers shut down. With this information we hope to find a correlation
between any of these forms of data to help us understand where and why these shutdowns
occurred due to DDoS attacks.
Excel Descriptive Statics
Company
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
DDoS
Attacks
5
2
10
4
6
12
5
6
4
3
9
8
11
13
4
5
7
8
12
3
15
8
4
6
9
7
5
14
7
6
Protective
Devices
1
0
10
5
5
15
10
2
4
5
5
10
15
19
5
7
12
15
20
5
20
16
9
17
13
6
8
18
17
6
Shutdown
N
N
Y
N
Y
Y
Y
Y
N
N
Y
Y
Y
Y
N
N
Y
N
Y
N
Y
N
N
Y
N
Y
N
N
N
Y
DDoS Attacks
Mean
Standard Error
Median
Mode
Stand Dev
Range
Minimum
Maximum
Sum
Count
Univariate
Graphic Displays
Bin_DDoS
ProtectiveDevices
7.27
0.63
6.50
5.00
3.45
13.00
2.00
15.00
218.00
30.00
10.00
1.10
9.50
5.00
6.00
20.00
0.00
20.00
300.00
30.00
Frequency
2
5
7
10
12
1
6
10
5
4
3
More
Frequency
DDoS Attack Histogram
15
10
5
Frequency
0
2
5
7
10
12 More
Number of DDoS Attacks
Bin_ProDev
Frequency
0
4
8
12
16
More
1
2
10
5
5
6
Frequency
Protected Device Histogram
15
10
5
Frequency
0
0
4
8
12
16 More
Number of Protected Devices
Subgroup Analysis - Repositioning Variable
Company
1
2
4
9
10
15
16
18
20
22
23
25
27
28
29
3
5
6
7
8
11
12
13
14
17
19
21
24
26
30
DDoS
Attacks
5
Protective
Devices
1
2
0
4
5
4
4
3
5
4
5
5
7
8
15
3
5
8
16
4
9
9
13
5
8
14
18
7
17
10
10
6
5
12
15
5
10
6
2
9
5
8
10
11
15
13
19
7
12
12
20
15
20
6
17
7
6
6
6
Shutdown
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Sort and Reposition
DDoS Shutdown Y
DDoS Shutdown N
10
5
6
2
12
4
5
4
6
3
9
4
8
5
11
8
13
3
7
8
12
4
15
9
6
5
7
14
6
7
Pro Dev Shutdown Y
Pro Dev Shutdown N
10
1
5
0
15
5
10
4
2
5
5
5
10
7
15
15
19
5
12
16
20
9
20
13
17
8
6
18
6
17
Descriptive Statistics for Subgroups
DDoS Shutdown Y
Mean
Standard Error
Median
Mode
Standard
Deviation
Range
Minimum
Maximum
Sum
Count
DDoS Shutdown N
8.87
0.80
8.00
6.00
5.67
0.80
5.00
4.00
3.11
10.00
5.00
15.00
133.00
15.00
3.09
12.00
2.00
14.00
85.00
15.00
Pro Dev Shutdown Y
Pro Dev Shutdown N
11.47
1.54
10.00
10.00
5.96
18.00
2.00
20.00
172.00
15.00
8.53
1.51
7.00
5.00
5.87
18.00
0.00
18.00
128.00
15.00
Mean
Standard Error
Median
Mode
Standard Deviation
Range
Minimum
Maximum
Sum
Count
Bar Charts for each Subgroup
Mean DDoS Attacks
DDoS Attacks by Shutdown
10.00
8.00
6.00
4.00
2.00
0.00
DDoS Shutdown Y
DDoS Shutdown N
Shutdowns per DDoS Attack
Mean Protected Devices
Protected Devices by Shutdown
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00
Pro Dev Shutdown Y
Pro Dev Shutdown N
Shutdowns per Protected Devices
SPSS DESCRIPTIVE STATISTICS
Statistics
DDoS Attacks
N
Valid
Protective Devices
Shutdown
30
30
30
0
0
0
Mean
7.267
10.000
Std. Error of Mean
.6305
1.0954
Median
6.500
9.500
4.0a
5.0
Std. Deviation
3.4535
6.0000
Variance
11.926
36.000
Skewness
.679
.202
Std. Error of Skewness
.427
.427
-.358
-1.208
Std. Error of Kurtosis
.833
.833
Range
13.0
20.0
Minimum
2.0
.0
Maximum
15.0
20.0
218.0
300.0
Missing
Mode
Kurtosis
Sum
a. Multiple modes exist. The smallest value is shown
Frequency Tables
DDoS Attacks
Frequency
Valid
Percent
Valid Percent
Cumulative Percent
2.0
1
3.3
3.3
3.3
3.0
2
6.7
6.7
10.0
4.0
4
13.3
13.3
23.3
5.0
4
13.3
13.3
36.7
6.0
4
13.3
13.3
50.0
7.0
3
10.0
10.0
60.0
8.0
3
10.0
10.0
70.0
9.0
2
6.7
6.7
76.7
10.0
1
3.3
3.3
80.0
11.0
1
3.3
3.3
83.3
12.0
2
6.7
6.7
90.0
13.0
1
3.3
3.3
93.3
14.0
1
3.3
3.3
96.7
15.0
1
3.3
3.3
100.0
Total
30
100.0
100.0
Protective Devices
Cumulative
Frequency
Valid
Percent
Valid Percent
Percent
.0
1
3.3
3.3
3.3
1.0
1
3.3
3.3
6.7
2.0
1
3.3
3.3
10.0
4.0
1
3.3
3.3
13.3
5.0
6
20.0
20.0
33.3
6.0
2
6.7
6.7
40.0
7.0
1
3.3
3.3
43.3
8.0
1
3.3
3.3
46.7
9.0
1
3.3
3.3
50.0
10.0
3
10.0
10.0
60.0
12.0
1
3.3
3.3
63.3
13.0
1
3.3
3.3
66.7
15.0
3
10.0
10.0
76.7
16.0
1
3.3
3.3
80.0
17.0
2
6.7
6.7
86.7
18.0
1
3.3
3.3
90.0
19.0
1
3.3
3.3
93.3
20.0
2
6.7
6.7
100.0
Total
30
100.0
100.0
Shutdown
Cumulative
Frequency
Valid
Percent
Valid Percent
Percent
N
15
50.0
50.0
50.0
Y
15
50.0
50.0
100.0
Total
30
100.0
100.0
Histograms
Shutdowns
Case Processing Summary
Cases
Valid
Shutdown
DDoS Attacks
Protective Devices
N
Missing
Percent
N
Total
Percent
N
Percent
N
15
100.0%
0
0.0%
15
100.0%
Y
15
100.0%
0
0.0%
15
100.0%
N
15
100.0%
0
0.0%
15
100.0%
Y
15
100.0%
0
0.0%
15
100.0%
Descriptives
Shutdown
DDoS Attacks
N
Statistic
Mean
5.667
95% Confidence Interval for
Lower Bound
3.958
Mean
Upper Bound
7.376
5% Trimmed Mean
5.407
Median
5.000
Variance
9.524
Std. Deviation
Minimum
2.0
Maximum
14.0
Range
12.0
4.0
Skewness
1.506
.580
Kurtosis
2.678
1.121
Mean
8.867
.8040
95% Confidence Interval for
Lower Bound
7.142
Mean
Upper Bound
10.591
5% Trimmed Mean
8.741
Median
8.000
Variance
9.695
Std. Deviation
3.1137
Minimum
5.0
Maximum
15.0
Range
10.0
Interquartile Range
6.0
Skewness
Protective Devices
N
.7968
3.0861
Interquartile Range
Y
Std. Error
.569
.580
Kurtosis
-.916
1.121
Mean
8.533
1.5146
95% Confidence Interval for
Lower Bound
5.285
Mean
Upper Bound
11.782
5% Trimmed Mean
8.481
Median
7.000
Variance
34.410
Std. Deviation
5.8660
Minimum
.0
Y
Maximum
18.0
Range
18.0
Interquartile Range
10.0
Skewness
.371
.580
Kurtosis
-1.171
1.121
Mean
11.467
1.5395
95% Confidence Interval for
Lower Bound
8.165
Mean
Upper Bound
14.769
5% Trimmed Mean
11.519
Median
10.000
Variance
35.552
Std. Deviation
5.9626
Minimum
2.0
Maximum
20.0
Range
18.0
Interquartile Range
11.0
Skewness
.079
.580
-1.300
1.121
Kurtosis
DDoS Histogram/Stem and Leaf
Protected Devices Histogram/Stem and Leaf
STATGRAPHICS DESCRIPTIVE STATISTICS
Multiple Variable Analysis
Data variables:
DDoS Attacks
Protective Devices
All available data will be used in each calculation.
The StatAdvisor
This procedure is designed to summarize several columns of quantitative data. It will calculate various statistics, including
correlations,
covariances, and partial correlations. Also included in the procedure are a number of multivariate graphs, which give interesting
views into
the data. Use the Tabular Options and Graphical Options buttons on the analysis toolbar to access these different procedures.
After this procedure, you may wish to select another procedure to build a statistical model for your data. Depending on your
goal, one of
several procedures may be appropriate. Following is a list of goals with an indication of which procedure would be appropriate:
GOAL: build a model for predicting one variable given values of one of more other variables.
PROCEDURE: Relate - Multiple Factors - Multiple Regression
GOAL: group rows of data with similar characteristics.
PROCEDURE: Describe - Multivariate Methods - Cluster Analysis
GOAL: develop a method for predicting which of several groups new rows belong to.
PROCEDURE: Relate - Classification Methods - Discriminant Analysis
GOAL: reduce the number of columns to a small set of meaningful measures.
PROCEDURE: Describe - Multivariate Methods - Factor Analysis
GOAL: determine which combinations of the columns determine most of the variability in your data.
PROCEDURE: Describe - Multivariate Methods - Principal Components
GOAL: find combinations of the columns which are strongly related to each other.
PROCEDURE: Describe - Multivariate Methods - Canonical Correlations
Shutdown
N
Y
DDoS Attacks
Protective Devices
Summary Statistics
Count
Average
Standard deviation
Coeff. of variation
Minimum
Maximum
Range
Stnd. skewness
Stnd. kurtosis
DDoS Attacks
30
7.26667
3.45347
47.5248%
2.0
15.0
13.0
1.51785
-0.400615
Protective Devices
30
10.0
6.0
60.0%
0
20.0
20.0
0.452079
-1.35112
The StatAdvisor
This table shows summary statistics for each of the selected data variables. It includes measures of central tendency, measures of
variability,
and measures of shape. Of particular interest here are the standardized skewness and standardized kurtosis, which can be used to
determine
whether the sample comes from a normal distribution. Values of these statistics outside the range of -2 to +2 indicate significant
departures
from normality, which would tend to invalidate many of the statistical procedures normally applied to this data. In this case, the
following
variables show standardized skewness values outside the expected range:
<none>
The following variables show standardized kurtosis values outside the expected range:
<none>
Correlations
DDoS Attacks
DDoS Attacks
Protective Devices
Protective Devices
0.7838
(30)
0.0000
0.7838
(30)
0.0000
Correlation
(Sample Size)
P-Value
The StatAdvisor
This table shows Pearson product moment correlations between each pair of variables. These correlation coefficients range
between -1 and +1
and measure the strength of the linear relationship between the variables. Also shown in parentheses is the number of pairs of
data values
used to compute each coefficient. The third number in each location of the table is a P-value which tests the statistical
significance of the
estimated correlations. P-values below 0.05 indicate statistically significant non-zero correlations at the 95.0% confidence level.
The
following pairs of variables have P-values below 0.05:
DDoS Attacks and Protective Devices
Two Sample Comparison - DDoS Attacks by Shutdown
Sample 1: Shutdown=N
Sample 2: Shutdown=Y
Sample 1: 15 values ranging from 2.0 to 14.0
Sample 2: 15 values ranging from 5.0 to 15.0
The StatAdvisor
This procedure is designed to compare two samples of data. It will calculate various statistics and graphs for each sample, and it
will run
several tests to determine whether there are statistically significant differences between the two samples.
N
6
frequency
4
2
0
2
4
6
0
4
Summary Statistics for DDoS Attacks
Shutdown=N
8
Y
Shutdown=Y
12
16
Count
Average
Standard deviation
Coeff. of variation
Minimum
Maximum
Range
Stnd. skewness
Stnd. kurtosis
15
5.66667
3.08607
54.46%
2.0
14.0
12.0
2.38045
2.11739
15
8.86667
3.11372
35.1171%
5.0
15.0
10.0
0.899294
-0.724131
The StatAdvisor
This table shows summary statistics for the two samples of data. Other tabular options within this analysis can be used to test
whether
differences between the statistics from the two samples are statistically significant. Of particular interest here are the
standardized skewness
and standardized kurtosis, which can be used to determine whether the samples come from normal distributions. Values of these
statistics
outside the range of -2 to +2 indicate significant departures from normality, which would tend to invalidate the tests which
compare the
standard deviations. In this case, Shutdown=N has a standardized skewness value outside the normal range. Shutdown=N has a
standardized kurtosis value outside the normal range.
Density Traces
0.15
Variables
Shutdown=N
Shutdown=Y
density
0.12
0.09
0.06
0.03
0
0
3
6
9
12
15
Comparison of Means for DDoS Attacks
95.0% confidence interval for mean of Shutdown=N: 5.66667 +/- 1.70901 [3.95766, 7.37568]
95.0% confidence interval for mean of Shutdown=Y: 8.86667 +/- 1.72432 [7.14234, 10.591]
95.0% confidence interval for the difference between the means
assuming equal variances: -3.2 +/- 2.31866 [-5.51866, -0.881338]
t test to compare means
Null hypothesis: mean1 = mean2
Alt. hypothesis: mean1 NE mean2
assuming equal variances: t = -2.82703 P-value = 0.008577
Reject the null hypothesis for alpha = 0.05.
The StatAdvisor
This option runs a t-test to compare the means of the two samples. It also constructs confidence intervals or bounds for each
mean and for the
difference between the means. Of particular interest is the confidence interval for the difference between the means, which
extends from
-5.51866 to -0.881338. Since the interval does not contain the value 0, there is a statistically significant difference between the
means of the
two samples at the 95.0% confidence level.
A t-test may also be used to test a specific hypothesis about the difference between the means of the populations from which the
two samples
come. In this case, the test has been constructed to determine whether the difference between the two means equals 0.0 versus
the alternative
hypothesis that the difference does not equal 0.0. Since the computed P-value is less than 0.05, we can reject the null hypothesis
in favor of
the alternative.
NOTE: these results assume that the variances of the two samples are equal. In this case, that assumption appears to be
reasonable based on
the results of an F-test to compare the standard deviations. You can see the results of that test by selecting Comparison of
Standard
Deviations from the Tabular Options menu.
Box-and-Whisker Plot
N
Y
0
3
6
9
DDoS Attacks
Comparison of Standard Deviations for DDoS Attacks
Shutdown=N
Shutdown=Y
Standard deviation
3.08607
3.11372
Variance
9.52381
9.69524
Df
14
14
Ratio of Variances = 0.982318
95.0% Confidence Intervals
Standard deviation of Shutdown=N: [2.25939, 4.86703]
Standard deviation of Shutdown=Y: [2.27964, 4.91064]
Ratio of Variances: [0.329793, 2.92592]
F-test to Compare Standard Deviations
Null hypothesis: sigma1 = sigma2
Alt. hypothesis: sigma1 NE sigma2
F = 0.982318 P-value = 0.973846
Do not reject the null hypothesis for alpha = 0.05.
12
15
The StatAdvisor
This option runs an F-test to compare the variances of the two samples. It also constructs confidence intervals or bounds for each
standard
deviation and for the ratio of the variances. Of particular interest is the confidence interval for the ratio of the variances, which
extends from
0.329793 to 2.92592. Since the interval contains the value 1, there is not a statistically significant difference between the
standard
deviations of the two samples at the 95.0% confidence level.
An F-test may also be used to test a specific hypothesis about the standard deviations of the populations from which the two
samples come. In
this case, the test has been constructed to determine whether the ratio of the standard deviations equals 1.0 versus the alternative
hypothesis
that the ratio does not equal 1.0. Since the computed P-value is not less than 0.05, we cannot reject the null hypothesis.
IMPORTANT NOTE: the F-tests and confidence intervals shown here depend on the samples having come from normal
distributions. To test
this assumption, select Summary Statistics from the list of Tabular Options and check the standardized skewness and
standardized kurtosis
values.
Two Sample Comparison - Protective Devices by Shutdown
Sample 1: Shutdown=N
Sample 2: Shutdown=Y
Sample 1: 15 values ranging from 0 to 18.0
Sample 2: 15 values ranging from 2.0 to 20.0
The StatAdvisor
This procedure is designed to compare two samples of data. It will calculate various statistics and graphs for each sample, and it
will run
several tests to determine whether there are statistically significant differences between the two samples.
N
5
frequency
3
1
1
3
5
-1
3
7
11
Y
15
19
23
Summary Statistics for Protective Devices
Shutdown=N
Count
15
Average
8.53333
Standard deviation
5.86596
Coeff. of variation
68.7418%
Minimum
0
Maximum
18.0
Range
18.0
Stnd. skewness
0.58683
Stnd. kurtosis
-0.925405
Shutdown=Y
15
11.4667
5.96258
51.9993%
2.0
20.0
18.0
0.124575
-1.02759
The StatAdvisor
This table shows summary statistics for the two samples of data. Other tabular options within this analysis can be used to test
whether
differences between the statistics from the two samples are statistically significant. Of particular interest here are the
standardized skewness
and standardized kurtosis, which can be used to determine whether the samples come from normal distributions. Values of these
statistics
outside the range of -2 to +2 indicate significant departures from normality, which would tend to invalidate the tests which
compare the
standard deviations. In this case, both standardized skewness values are within the range expected. Both standardized kurtosis
values are
within the range expected.
Density Traces
0.08
Variables
Shutdown=N
Shutdown=Y
density
0.06
0.04
0.02
0
0
4
8
12
16
20
Comparison of Means for Protective Devices
95.0% confidence interval for mean of Shutdown=N: 8.53333 +/- 3.24847 [5.28486, 11.7818]
95.0% confidence interval for mean of Shutdown=Y: 11.4667 +/- 3.30197 [8.16469, 14.7686]
95.0% confidence interval for the difference between the means
assuming equal variances: -2.93333 +/- 4.42387 [-7.3572, 1.49054]
t test to compare means
Null hypothesis: mean1 = mean2
Alt. hypothesis: mean1 NE mean2
assuming equal variances: t = -1.35824 P-value = 0.185232
Do not reject the null hypothesis for alpha = 0.05.
The StatAdvisor
This option runs a t-test to compare the means of the two samples. It also constructs confidence intervals or bounds for each
mean and for the
difference between the means. Of particular interest is the confidence interval for the difference between the means, which
extends from -7.3572
to 1.49054. Since the interval contains the value 0, there is not a statistically significant difference between the means of the two
samples at
the 95.0% confidence level.
A t-test may also be used to test a specific hypothesis about the difference between the means of the populations from which the
two samples
come. In this case, the test has been constructed to determine whether the difference between the two means equals 0.0 versus
the alternative
hypothesis that the difference does not equal 0.0. Since the computed P-value is not less than 0.05, we cannot reject the null
hypothesis.
NOTE: these results assume that the variances of the two samples are equal. In this case, that assumption appears to be
reasonable based on
the results of an F-test to compare the standard deviations. You can see the results of that test by selecting Comparison of
Standard
Deviations from the Tabular Options menu.
Box-and-Whisker Plot
N
Y
0
4
8
12
Protective Devices
Comparison of Standard Deviations for Protective Devices
Shutdown=N
Shutdown=Y
Standard deviation
5.86596
5.96258
Variance
34.4095
35.5524
Df
14
14
Ratio of Variances = 0.967854
95.0% Confidence Intervals
Standard deviation of Shutdown=N: [4.29463, 9.25119]
Standard deviation of Shutdown=Y: [4.36536, 9.40357]
Ratio of Variances: [0.324937, 2.88284]
F-test to Compare Standard Deviations
Null hypothesis: sigma1 = sigma2
Alt. hypothesis: sigma1 NE sigma2
F = 0.967854 P-value = 0.95212
Do not reject the null hypothesis for alpha = 0.05.
16
20
The StatAdvisor
This option runs an F-test to compare the variances of the two samples. It also constructs confidence intervals or bounds for each
standard
deviation and for the ratio of the variances. Of particular interest is the confidence interval for the ratio of the variances, which
extends from
0.324937 to 2.88284. Since the interval contains the value 1, there is not a statistically significant difference between the
standard
deviations of the two samples at the 95.0% confidence level.
An F-test may also be used to test a specific hypothesis about the standard deviations of the populations from which the two
samples come. In
this case, the test has been constructed to determine whether the ratio of the standard deviations equals 1.0 versus the alternative
hypothesis
that the ratio does not equal 1.0. Since the computed P-value is not less than 0.05, we cannot reject the null hypothesis.
IMPORTANT NOTE: the F-tests and confidence intervals shown here depend on the samples having come from normal
distributions. To test
this assumption, select Summary Statistics from the list of Tabular Options and check the standardized skewness and
standardized kurtosis
values.
One Variable Analysis - DDoS Attacks
Data variable: DDoS Attacks
30 values ranging from 2.0 to 15.0
The StatAdvisor
This procedure is designed to summarize a single sample of data. It will calculate various statistics and graphs. Also included in
the
procedure are confidence intervals and hypothesis tests. Use the Tabular Options and Graphical Options buttons on the analysis
toolbar to
access these different procedures.
Histogram
4
frequency
3
2
1
0
0
4
8
DDoS Attacks
Frequency Tabulation for DDoS Attacks
Lower
Upper
Class Limit
Limit
Midpoint
at or below
0
1
0
1.06667
0.533333
2
1.06667
2.13333
1.6
3
2.13333
3.2
2.66667
4
3.2
4.26667
3.73333
12
Frequency
0
0
1
2
4
16
Relative
Frequency
0.0000
0.0000
0.0333
0.0667
0.1333
Cumulative
Frequency
0
0
1
3
7
Cum. Rel.
Frequency
0.0000
0.0000
0.0333
0.1000
0.2333
5
6
7
8
9
10
11
12
13
14
15
4.26667
5.33333
4.8
5.33333
6.4
5.86667
6.4
7.46667
6.93333
7.46667
8.53333
8.0
8.53333
9.6
9.06667
9.6
10.6667
10.1333
10.6667
11.7333
11.2
11.7333
12.8
12.2667
12.8
13.8667
13.3333
13.8667
14.9333
14.4
14.9333
16.0
15.4667
above
16
Mean = 7.26667 Standard deviation = 3.45347
4
4
3
3
2
1
1
2
1
1
1
0
0.1333
0.1333
0.1000
0.1000
0.0667
0.0333
0.0333
0.0667
0.0333
0.0333
0.0333
0.0000
11
15
18
21
23
24
25
27
28
29
30
30
0.3667
0.5000
0.6000
0.7000
0.7667
0.8000
0.8333
0.9000
0.9333
0.9667
1.0000
1.0000
The StatAdvisor
This option performs a frequency tabulation by dividing the range of DDoS Attacks into equal width intervals and counting the
number of
data values in each interval. The frequencies show the number of data values in each interval, while the relative frequencies
show the
proportions in each interval. You can change the definition of the intervals by pressing the alternate mouse button and selecting
Pane
Options. You can see the results of the tabulation graphically by selecting Frequency Histogram from the list of Graphical
Options.
One Variable Analysis - Protective Devices
Data variable: Protective Devices
30 values ranging from 0 to 20.0
The StatAdvisor
This procedure is designed to summarize a single sample of data. It will calculate various statistics and graphs. Also included in
the
procedure are confidence intervals and hypothesis tests. Use the Tabular Options and Graphical Options buttons on the analysis
toolbar to
access these different procedures.
Histogram
8
frequency
6
4
2
0
-1
3
7
11
15
Protective Devices
Frequency Tabulation for Protective Devices
Lower
Upper
Class Limit
Limit
Midpoint
at or below
0
1
0
0.6
-0.2
2
0.6
2.2
1.4
3
2.2
3.8
3.0
Frequency
0
1
2
0
19
23
Relative
Frequency
0.0000
0.0333
0.0667
0.0000
Cumulative
Frequency
0
1
3
3
Cum. Rel.
Frequency
0.0000
0.0333
0.1000
0.1000
4
5
6
7
8
9
10
11
12
13
14
15
3.8
5.4
4.6
5.4
7.0
6.2
7
8.6
7.8
8.6
10.2
9.4
10.2
11.8
11.0
11.8
13.4
12.6
13.4
15.0
14.2
15
16.6
15.8
16.6
18.2
17.4
18.2
19.8
19.0
19.8
21.4
20.6
21.4
23.0
22.2
above
23
Mean = 10.0 Standard deviation = 6.0
7
3
1
4
0
2
3
1
3
1
2
0
0
0.2333
0.1000
0.0333
0.1333
0.0000
0.0667
0.1000
0.0333
0.1000
0.0333
0.0667
0.0000
0.0000
10
13
14
18
18
20
23
24
27
28
30
30
30
0.3333
0.4333
0.4667
0.6000
0.6000
0.6667
0.7667
0.8000
0.9000
0.9333
1.0000
1.0000
1.0000
The StatAdvisor
This option performs a frequency tabulation by dividing the range of Protective Devices into equal width intervals and counting
the number
of data values in each interval. The frequencies show the number of data values in each interval, while the relative frequencies
show the
proportions in each interval. You can change the definition of the intervals by pressing the alternate mouse button and selecting
Pane
Options. You can see the results of the tabulation graphically by selecting Frequency Histogram from the list of Graphical
Options.
With all of the information we were given we were able to find the descriptive statistics of each
set of data compared to each other. The statistics we received includes the mean, median, modes,
standard variation, range, minimum, maximum, sum, and count, along with their frequencies. There
have also been visual representations of the data compared such as histograms, stem and leaf plots, box
and whisker plots, frequency tables, and density traces. Using the information that has been gathered it
is now possible to identify what correlations each set of data has to help understand why certain servers
were being shut down by DDoS attacks with or without protected devices.