Descriptive Statistics Analysis
MAMA0611
UnitIVScholarlyActivity-CorrectionsNeeded.pdf
Unit IV – Scholarly Activity – Statistics Analysis 2
Descriptive Statistics and Assumption Testing
Correlation: Descriptive Statistics and Assumption Testing
Frequency Distribution Table
Bins Frequenc
y
2 1
3 1
4 5
5 13
6 18
7 24
8 18
9 12
10 7
11 2
12 2
Histogram
2 3 4 5 6 7 8 9 10 11 12 0
5
10
15
20
25
30
Histogram
Series1
Mean annual sick days per employee
F re
q u
e n
cy
Unit IV – Scholarly Activity – Statistics Analysis 3
Descriptive Statistics Table
job site microns
mean annual sick days per
employee
Mean 52 Mean 5.65728
2 Mean 7.126213592
Standard Error 2.94392 Standard Error 0.2556 Standard Error 0.186483898
Median 52 Median 6 Median 7
Mode #N/A Mode 8 Mode 7 Standard Deviation
29.8775 3
Standard Deviation
2.59405 8
Standard Deviation 1.892604864
Sample Variance 892.666
7 Sample Variance 6.72913
8 Sample Variance 3.58195317
Kurtosis -1.2 Kurtosis -0.85216 Kurtosis 0.124922603
Skewness -3.6E-17 Skewness -0.37326 Skewness 0.142249784
Range 102 Range 9.8 Range 10
Minimum 1 Minimum 0.2 Minimum 2
Maximum 103 Maximum 10 Maximum 12
Sum 5356 Sum 582.7 Sum 734
Count 103 Count 103 Count 103
Measurement Scale
Job site is a nominal measurement of scale since the difference, addition, multiplication of
variables cannot be established. Microns is an ordinal measurement of scale.
Measure of Central Tendency
The mean of the microns is 5.65, the median is 6 and the mode is 8.
Skewness and Kurtosis
The data is skewed to the right since it has a positive value.
Evaluation
The annual mean sick days for employee had a mean of 7.126. The mode was 7 and the
median was also 7. The maximum sick days for employees was 12 and the minimum sick days was
Unit IV – Scholarly Activity – Statistics Analysis 4
two. The assumptions for parametric statistical were not met since data from multiple groups had
different variance.
Simple Regression: Descriptive Statistics and Assumption Testing
Frequency Distribution Table
Bins Frequenc y
10 1
20 0
30 1
40 3
50 1
60 5
70 6
80 3
90 4
100 8
110 5
120 10
130 8
140 11
150 10
160 3
170 4
180 11
190 29
200 7
210 13
220 6
230 17
240 8
250 11
260 3
270 3
280 11
Unit IV – Scholarly Activity – Statistics Analysis 5
290 9
300 4
310 0
320 2
330 2
340 3
350 0
360 1
Histogram
10 30 50 70 90 11 0
13 0
15 0
17 0
19 0
21 0
23 0
25 0
27 0
29 0
31 0
33 0
35 0
0
5
10
15
20
25
30
35
Histogram
Series1
Lost time hours
F re
q u
e n
cy
Descriptive Statistics Table
contract # safety training
expenditure lost time hours
Mean 358.278 Mean 595.984
4 Mean 188.004
5
Standard Error 39.4095 Standard Error 31.4770
1 Standard Error 4.80308
9
Median 145 Median 507.772 Median 190
Mode 205 Mode 234 Mode 190 Standard Deviation
588.509 3
Standard Deviation 470.052
Standard Deviation
71.7254 2
Sample Variance 346343.
2 Sample Variance 220948.
8 Sample Variance 5144.53
6
Kurtosis 5.10620
5 Kurtosis 0.44408 Kurtosis -0.50122
Unit IV – Scholarly Activity – Statistics Analysis 6
Skewness 2.45654
1 Skewness 0.95133
2 Skewness -0.08198
Range 2799 Range 2251.40
4 Range 350
Minimum 2 Minimum 20.456 Minimum 10
Maximum 2801 Maximum 2271.86 Maximum 360
Sum 79896 Sum 132904.
5 Sum 41925
Count 223 Count 223 Count 223
Measurement Scale
The measurement of scale used was nominal.
Measure of Central Tendency
The mean for lost hours was 188.0045, the median was 190 and the mode was 190. The less they
spend in training the more employees get sick.
Skewness and Kurtosis
The lost time hours data is skewed to the left. The distribution is light tailed.
Evaluation
The distribution in this case indicates a summary of the frequency of individual values. The
mean for lost hours was 188.0045, the median was 190 and the mode was 190. The standard
deviation is 71.725 which means approximately 68% of the lost time hours fall within its mean.
The assumption for parametric statistical testing were not met since the data did not have a normal
distribution.
Multiple Regression: Descriptive Statistics and Assumption Testing
Frequency Distribution Table
Unit IV – Scholarly Activity – Statistics Analysis 7
Bins Frequenc y
31.5 0
34 281
36.5 0
39 0
41.5 480
44 0
46.5 0
49 0
51.5 0
54 0
56.5 277
59 0
61.5 0
64 0
66.5 0
69 0
71.5 465
Histogram
31.5 34 36.5 39 41.5 44 46.5 49 51.5 54 56.5 59 61.5 64 66.5 69 71.5 0
100
200
300
400
500
600
Histogram
Series1
Velocity
F re
q u
e n
cy
Descriptive Statistics Table
contra Frequ Angle Chord Velocity Displa Decib
Unit IV – Scholarly Activity – Statistics Analysis 8
ct # ency (Hz)
in Degre
es Lengt
h
(Meters per
Second) ceme
nt el
Mean
34 1.0 62
5 Mean
28 86. 38
1 Mean
6.7 82 30
2 Mean
0.1 16 14 Mean
50. 86 07
5 Mean
0.0 11 14 Mean
12 4.8 35
9
Stand ard Error
14. 68 41
2
Stand ard Error
81. 31 78
1
Stand ard Error
0.1 52 65
3
Stand ard Error
0.0 01 25
6 Standard Error
0.4 01 68
6
Stand ard Error
0.0 00 33
9
Stand ard Error
0.1 77 94
5
Media n
14 3
Media n
16 00
Media n 5.4
Media n
0.1 17
6 Median 39.
6 Media n
0.0 04 95
7 Media n
12 5.7 21
Mode 15
7 Mode 20 00 Mode 0 Mode
0.0 91
7 Mode 39.
6 Mode
0.0 05 29
5 Mode
12 7.3 15
Stand ard Devia tion
56 9.2 81
8
Stand ard Devia tion
31 52. 57
3
Stand ard Devia tion
5.9 18 12
8
Stand ard Devia tion
0.0 48 70
8 Standard Deviation
15. 57 27
8
Stand ard Devia tion
0.0 13 15
Stand ard Devia tion
6.8 98 65
7 Sampl e Varian ce
32 40
81. 7
Sampl e Varian ce
99 38 71
7
Sampl e Varian ce
35. 02 42
4
Sampl e Varian ce
0.0 02 37
2 Sample Variance
24 2.5 11
6
Sampl e Varian ce
0.0 00 17
3
Sampl e Varian ce
47. 59 14
6
Kurtos is
5.4 48 48
1 Kurtos is
5.7 08 68
5 Kurtos is
- 0.4 12 95
Kurtos is
- 1.1 78
2 Kurtosis
- 1.5 63 95
Kurtos is
2.2 18 90
3 Kurtos is
- 0.3 14 19
Skewn ess
2.5 39 71
1 Skewn ess
2.1 37 08
4 Skewn ess
0.6 89 16
4 Skewn ess
- 0.0 27 54 Skewness
0.2 35 85
2 Skewn ess
1.7 02 16
5 Skewn ess
- 0.4 18 95
Range 27 99 Range
19 80
0 Range 22.
2 Range
0.1 69
7 Range 39.
6 Range
0.0 58 01
1 Range
37. 60
7
Minim um 2
Minim um
20 0
Minim um 0
Minim um
0.0 3 Minimum
31. 7
Minim um
0.0 00 40
1 Minim um
10 3.3
8 Maxi mum
28 01
Maxi mum
20 00
0
Maxi mum
22. 2
Maxi mum
0.1 99
7
Maximu m
71. 3
Maxi mum
0.0 58 41
Maxi mum
14 0.9 87
Unit IV – Scholarly Activity – Statistics Analysis 9
1
Sum
51 26 17 Sum
43 38 23
0 Sum
10 19
3.8 Sum
17 4.5 58
5 Sum
76 44
3.7 Sum
16. 74 32
4 Sum
18 76
28. 4
Count 15 03 Count
15 03 Count
15 03 Count
15 03 Count
15 03 Count
15 03 Count
15 03
Measurement Scale
The measurement of scale used was nominal.
Measure of Central Tendency
The velocity mean was 50.86, the median was 39.6 while the mode was 39.6.
Skewness and Kurtosis
The data set is skewed to the right. The data has a heavy tailed distribution. Both the skewness and
Kurtosis were within acceptable range.
Evaluation
The distribution in this case indicates a summary of the frequency of individual values. The
mean for velocity was 50.86, the median was 39.6 and the mode was 39.6. The standard deviation
is 15.57. The assumption for parametric statistical testing were not met since the data did not have
a normal distribution.
Independent Samples t Test: Descriptive Statistics and Assumption Testing
Frequency Distribution Table
Bin Frequen
cy
50 4 56.714
29 6
Unit IV – Scholarly Activity – Statistics Analysis 10
63.428 57 7
70.142 86 15
76.857 14 16
83.571 43 33
90.285 71 34
More 9
Histogram
50
56 .7
14 28
57 1
63 .4
28 57
14 3
70 .1
42 85
71 4
76 .8
57 14
28 6
83 .5
71 42
85 7
90 .2
85 71
42 9
M or
e
0
20
40
Histogram
Frequency
Prior training Scores
F re
q u
e n
cy
Descriptive Statistics Table
Group A Prior Training Scores
Group B Revised Training Scores
Mean 69.7903
2 Mean 84.7741
9
Standard Error 1.40278
8 Standard Error 0.65947
9
Median 70 Median 85
Mode 80 Mode 85 Standard Deviation
11.0455 6
Standard Deviation
5.19274 2
Unit IV – Scholarly Activity – Statistics Analysis 11
Sample Variance 122.004
5 Sample Variance 26.9645
7
Kurtosis -0.77668 Kurtosis -0.35254
Skewness -0.0868 Skewness 0.14408
5
Range 41 Range 22
Minimum 50 Minimum 75
Maximum 91 Maximum 97
Sum 4327 Sum 5256
Count 62 Count 62
Measurement Scale
The measurement of scale used was ratio since the sequence of variables, mode, median, mean,
difference between variables, addition, subtraction, multiplication, and division can be established.
Measure of Central Tendency
The mean for group A was 69.79 while that for group B was 84.77, the median for group A was 70
while that for group B was 85, while the mode for group A 80 and for group B was 85.
Skewness and Kurtosis
The data for group A is slightly skewed to the left while the data for group B is slightly skewed to
the right. Both data sets have light tailed distribution.
Evaluation
The distribution in this case indicates a summary of the frequency of individual values. The
mean, median, and mode of both data sets are nearly the same. The assumption for parametric
statistical testing were not met since the data did not have a normal distribution.
Dependent Samples (Paired-Samples) t Test: Descriptive Statistics and Assumption Testing
Frequency Distribution Table
Unit IV – Scholarly Activity – Statistics Analysis 12
Bin Frequen
cy
6 2 13.142
86 6 20.285
71 10 27.428
57 12 34.571
43 16 41.714
29 24 48.857
14 20
More 8
Histogram
6
13 .1
42 85
71 4
20 .2
85 71
42 9
27 .4
28 57
14 3
34 .5
71 42
85 7
41 .7
14 28
57 1
48 .8
57 14
28 6
M or
e
0
15
30
Histogram
Frequency
Employee Exposure
F re
q u
e n
cy
Descriptive Statistics Table
Employee Pre-Exposure
μg/dL Post-Exposure
μg/dL
Unit IV – Scholarly Activity – Statistics Analysis 13
Mean 25 Mean 32.8571
4 Mean 33.2857
1
Standard Error 2.04124
1 Standard Error 1.75230
7 Standard Error 1.78142
3
Median 25 Median 35 Median 36
Mode #N/A Mode 36 Mode 38 Standard Deviation
14.2886 9
Standard Deviation
12.2661 5
Standard Deviation
12.4699 6
Sample Variance 204.166
7 Sample Variance 150.458
3 Sample Variance 155.5
Kurtosis -1.2 Kurtosis -0.57604 Kurtosis -0.65421
Skewness -5.8E-17 Skewness -0.42511 Skewness -0.48363
Range 48 Range 50 Range 50
Minimum 1 Minimum 6 Minimum 6
Maximum 49 Maximum 56 Maximum 56
Sum 1225 Sum 1610 Sum 1631
Count 49 Count 49 Count 49
Measurement Scale
The measurement of scale used was nominal.
Measure of Central Tendency
The mean for pre-exposure was 32.86, and for post-exposure 33.29. The median for pre-exposure
is 35, and for post exposure is 36. The mode for pre-exposure is 36 while that of post exposure is
38.
Skewness and Kurtosis
Both data sets are skewed to the left. The data has a heavy tailed distribution. Both the skewness
and Kurtosis were within acceptable range.
Evaluation
The distribution in this case indicates a summary of the frequency of individual values. The
mean, median, and mode of both data sets are nearly the same. The assumption for parametric
statistical testing were not met since the data did not have a normal distribution.
Unit IV – Scholarly Activity – Statistics Analysis 14
ANOVA: Descriptive Statistics and Assumption Testing
Frequency Distribution Table
Bin Frequenc
y
3 3
5.75 18
8.5 30
11.25 21
More 8
Histogram
3 5.75 8.5 11.25 More 0
10
20
30
40
Histogram
Frequency
Consulting Project Return on investment
F re
q u
e n
cy
Descriptive Statistics Table
A = Air B = Soil C = Water D = Training
Mean 8.9 Mean 9.1 Mean 7 Mean 5.4
Unit IV – Scholarly Activity – Statistics Analysis 15
Standard Error
0.68402 8
Standard Error
0.39000 7
Standard Error
0.57582 9
Standard Error
0.26556 8
Median 9 Median 9 Median 6 Median 5
Mode 11 Mode 8 Mode 6 Mode 5 Standard Deviation
3.05906 8
Standard Deviation
1.74416 3
Standard Deviation
2.57518 5
Standard Deviation
1.18765 6
Sample Variance
9.35789 5
Sample Variance
3.04210 5
Sample Variance
6.63157 9
Sample Variance
1.41052 6
Kurtosis -0.6283 Kurtosis 0.11923 Kurtosis -
0.23752 Kurtosis 0.25374
7
Skewness -
0.36085 Skewness 0.49200
2 Skewness 0.76020
6 Skewness 0.15918
3
Range 11 Range 7 Range 9 Range 5
Minimum 3 Minimum 6 Minimum 3 Minimum 3
Maximum 14 Maximum 13 Maximum 12 Maximum 8
Sum 178 Sum 182 Sum 140 Sum 108
Count 20 Count 20 Count 20 Count 20
Measurement Scale
The measurement of scale used here was ratio
Measure of Central Tendency
The mean for return on investment on air was 8.9. The median was 9 while the mode was 11
Skewness and Kurtosis
All the data was skewed to the right. Both the skewness and Kurtosis were outside acceptable
range.
Evaluation
The distribution in this case indicates a summary of the frequency of individual values. The
mean, median, and mode of both data sets are nearly the same. The assumption for parametric
statistical testing were not met since the data did not have a normal distribution.
Unit IV – Scholarly Activity – Statistics Analysis 16
References
Fisher, M. J., & Marshall, A. P. (2009). Understanding descriptive statistics. Australian critical care, 22(2),
93-97.
Nick, T. G. (2007). Descriptive statistics. Topics in biostatistics, 33-52.
