Mat 540 Assignment 1
TASK 1: GETTING A HAND ON DATA
ORGANISING YOUR DATA:
A. Summarise your results in a table.
Name
Age
Writing Hand R/L?
Writing hand angle
Non-writing hand angles
Right (√)
Left (√)
Zac Taylor
15
√
50o
50o
Eric Na
17
√
55o
52o
Damian Bielinski
15
√
49o
48o
Ashley Vandenput
15
√
47o
50o
Tolga Pasin
15
√
50.5o
53o
Corey Evans
15
√
52o
50o
Romy Abbott
14
√
50o
53o
Candice Shadford
15
√
45o
54o
Jess Dayus
14
√
50o
55o
Joel Dayus
11
√
49o
55o
Myriam Dayus
42
√
58o
45o
Toby Abbott
16
√
53o
52o
B. Arrange your data in numerical order.
C. Calculate the five number summaries and summarise this information in a table.
D. ANALYSING …show more content…
THE DATA:
a) Select three (3) categories from those above and construct parallel box plots from your five number summaries.
b) Provide printouts of the three parallel boxplots.
E. Write a 300 word (approx) detailed analysis of the parallel boxplots.
Twelve people were tested on the angles of their writing and non-writing hand. These people aged through from eleven (11) to forty two (42), the data obtained was put into tables and a box plot diagram. A box plot is a diagram used to represent the range, median and quartiles of a set of data values. The difference between males and females will be compared, along with the shape of distribution of the diagram and the range. The three sets of data that were chosen to compare were the writing hand, males writing hand and females writing hand. These three were chosen as they all have a similar topic (writing hand) and will be easily compared and contrasted in regards to correlations between gender and the angles of writing hands.
The first box plot is almost double in length than the other two; this is because it had the data from both males and females rather than one or the other like the other two. It also had a large range, though the upper and lower quartiles were close to the beginning and end (minimum and maximum) of the box plot which caused the shape of distribution to be rather close and not very spread. Looking below to the second box plot, the first thing you notice is that it seems as though it is lacking a minimum. This is due to the minimum angle being the same as the lower quartile angle. With both angles being 49o, the shape of distribution becomes slightly off and is missing the distinctive line for the minimum. The range of the male writing hand is also noticeably smaller than the other two, this shows that on average males hands are more alike than females. The last box plot has a minimum and maximum that are further away from the upper and lower quartiles and the median.
This causes the shape of the box plot to be quite spread out with the median and quartiles close together. The female writing hand box plot is also the same length as the writing hand box plot; this is because the minimum and maximum data from the writing hand came from females. When putting the male and female writing hand box plots in comparison to each other, you can see that females have a much larger range than the males as discussed before. This causes the female box plot to have a lower, lower quartile and median and a higher upper quartile. The median for males is only slightly higher than the median for females, keeping in mind that males had data from an eleven (11) year old and females had data from a forty two (42) year old. This can cause the data to be slightly swayed as there were not equal age groups for both box …show more content…
plots. Overall males had a higher minimum, lower quartile and median and a lower maximum and upper quartile. It was interesting that females had a higher maximum than the males though the female maximum was from the forty two (42) year old. It was not expected that female maximum would be higher than males but it is reversed in the median where the male median is slightly higher than the females.
TASK 2: FORENSIC FORMULAS
A.
Draw three different scatter plots.
B. Fit a line of good fit to the points
C. Determine a rule. Write rule clearly on your scatterplot
Head circumference was chosen as the predictor as it has the lowest deviation out of the three.
Rule: y = 3.5154x - 33.215
D. Analysing the data.
Overall a majority of the points are either on or close to the line, with only a couple ranging out slightly further away from the line. The graph comparing height and head circumference has more points that are 'close' to the line compared to the other two graphs. The reasoning to this is that there were fewer variations in the data from individuals. Seven points are below the trend line, five are above and three are sitting exactly on the trend line. The spread is overall fairly even on each side of the trend line, though below the trend line the points are slightly more spaced out than the points above the trend line.
Head circumference (x)
Height (y)
Predicted height
Deviation (ignoring sign)
64
193
191.7706
1.2294
61
174
181.2244
-7.2244
62
184
184.7398
-0.7398
57
187
167.1628
19.8372
55
172
160.132
11.868
55
169
160.132
8.868
55
168
160.132
7.868
57
160
167.1628
-7.1628
61
179
181.2244
-2.2244
58
188
170.6782
17.3218
59
178
174.1936
3.8064
58
167
170.6782
-3.6782
57
177
167.1628
9.8372
57
181
167.1628
13.8372
54
161
156.6166
4.3834 Total deviations = 119.8862
Total deviations / 15 = 7.992413
TASK 3: INVESTIGATING DATA
i) The line appears to fit the data well, especially the predicted height data as every point comes into contact with the trend line. There were some slight variations with the actual height, particularly above the trend line, but apart from that most points are fairly close together and to the trend line. ii) Head circumference (x)
Height (y)
Predicted height
Deviation
64
193
188.832
4.168
61
174
182.349
-8.349
62
184
184.51
-0.51
57
187
173.705
13.295
55
172
169.383
2.617
55
169
169.383
-0.383
55
168
169.383
-1.383
57
160
173.705
-13.705
61
179
182.349
-3.349
58
188
175.866
12.134
59
178
178.027
-0.027
58
167
175.866
-8.866
57
177
173.705
3.295
57
181
173.705
7.295
54
161
167.222
-6.222
iii) The average deviation for the data from task three was 5.70653333. The average deviation from task two was 7.992413. There is only a slight different between the two; the reason for this is due to different sets of data being used in each task, causing the results to slightly vary.
TASK 4: FORENSIC INVESTIGATION
Rule: y = 2.161x + 50.528
Predicted height= 171.544
The predicted height was calculated by using the equation that was found earlier. (Y) was the predicted height and (x) was the head circumference. The measurement for head circumference (56cm) was substituted into the equation (y=2.161x+50.528) and therefore predicting what the height would have been.
ORGANISING YOUR DATA:
A. Summarise your results in a table.
Name
Age
Writing Hand R/L?
Writing hand angle
Non-writing hand angles
Right (√)
Left (√)
Zac Taylor
15
√
50o
50o
Eric Na
17
√
55o
52o
Damian Bielinski
15
√
49o
48o
Ashley Vandenput
15
√
47o
50o
Tolga Pasin
15
√
50.5o
53o
Corey Evans
15
√
52o
50o
Romy Abbott
14
√
50o
53o
Candice Shadford
15
√
45o
54o
Jess Dayus
14
√
50o
55o
Joel Dayus
11
√
49o
55o
Myriam Dayus
42
√
58o
45o
Toby Abbott
16
√
53o
52o
B. Arrange your data in numerical order.
C. Calculate the five number summaries and summarise this information in a table.
D. ANALYSING …show more content…
THE DATA:
a) Select three (3) categories from those above and construct parallel box plots from your five number summaries.
b) Provide printouts of the three parallel boxplots.
E. Write a 300 word (approx) detailed analysis of the parallel boxplots.
Twelve people were tested on the angles of their writing and non-writing hand. These people aged through from eleven (11) to forty two (42), the data obtained was put into tables and a box plot diagram. A box plot is a diagram used to represent the range, median and quartiles of a set of data values. The difference between males and females will be compared, along with the shape of distribution of the diagram and the range. The three sets of data that were chosen to compare were the writing hand, males writing hand and females writing hand. These three were chosen as they all have a similar topic (writing hand) and will be easily compared and contrasted in regards to correlations between gender and the angles of writing hands.
The first box plot is almost double in length than the other two; this is because it had the data from both males and females rather than one or the other like the other two. It also had a large range, though the upper and lower quartiles were close to the beginning and end (minimum and maximum) of the box plot which caused the shape of distribution to be rather close and not very spread. Looking below to the second box plot, the first thing you notice is that it seems as though it is lacking a minimum. This is due to the minimum angle being the same as the lower quartile angle. With both angles being 49o, the shape of distribution becomes slightly off and is missing the distinctive line for the minimum. The range of the male writing hand is also noticeably smaller than the other two, this shows that on average males hands are more alike than females. The last box plot has a minimum and maximum that are further away from the upper and lower quartiles and the median.
This causes the shape of the box plot to be quite spread out with the median and quartiles close together. The female writing hand box plot is also the same length as the writing hand box plot; this is because the minimum and maximum data from the writing hand came from females. When putting the male and female writing hand box plots in comparison to each other, you can see that females have a much larger range than the males as discussed before. This causes the female box plot to have a lower, lower quartile and median and a higher upper quartile. The median for males is only slightly higher than the median for females, keeping in mind that males had data from an eleven (11) year old and females had data from a forty two (42) year old. This can cause the data to be slightly swayed as there were not equal age groups for both box …show more content…
plots. Overall males had a higher minimum, lower quartile and median and a lower maximum and upper quartile. It was interesting that females had a higher maximum than the males though the female maximum was from the forty two (42) year old. It was not expected that female maximum would be higher than males but it is reversed in the median where the male median is slightly higher than the females.
TASK 2: FORENSIC FORMULAS
A.
Draw three different scatter plots.
B. Fit a line of good fit to the points
C. Determine a rule. Write rule clearly on your scatterplot
Head circumference was chosen as the predictor as it has the lowest deviation out of the three.
Rule: y = 3.5154x - 33.215
D. Analysing the data.
Overall a majority of the points are either on or close to the line, with only a couple ranging out slightly further away from the line. The graph comparing height and head circumference has more points that are 'close' to the line compared to the other two graphs. The reasoning to this is that there were fewer variations in the data from individuals. Seven points are below the trend line, five are above and three are sitting exactly on the trend line. The spread is overall fairly even on each side of the trend line, though below the trend line the points are slightly more spaced out than the points above the trend line.
Head circumference (x)
Height (y)
Predicted height
Deviation (ignoring sign)
64
193
191.7706
1.2294
61
174
181.2244
-7.2244
62
184
184.7398
-0.7398
57
187
167.1628
19.8372
55
172
160.132
11.868
55
169
160.132
8.868
55
168
160.132
7.868
57
160
167.1628
-7.1628
61
179
181.2244
-2.2244
58
188
170.6782
17.3218
59
178
174.1936
3.8064
58
167
170.6782
-3.6782
57
177
167.1628
9.8372
57
181
167.1628
13.8372
54
161
156.6166
4.3834 Total deviations = 119.8862
Total deviations / 15 = 7.992413
TASK 3: INVESTIGATING DATA
i) The line appears to fit the data well, especially the predicted height data as every point comes into contact with the trend line. There were some slight variations with the actual height, particularly above the trend line, but apart from that most points are fairly close together and to the trend line. ii) Head circumference (x)
Height (y)
Predicted height
Deviation
64
193
188.832
4.168
61
174
182.349
-8.349
62
184
184.51
-0.51
57
187
173.705
13.295
55
172
169.383
2.617
55
169
169.383
-0.383
55
168
169.383
-1.383
57
160
173.705
-13.705
61
179
182.349
-3.349
58
188
175.866
12.134
59
178
178.027
-0.027
58
167
175.866
-8.866
57
177
173.705
3.295
57
181
173.705
7.295
54
161
167.222
-6.222
iii) The average deviation for the data from task three was 5.70653333. The average deviation from task two was 7.992413. There is only a slight different between the two; the reason for this is due to different sets of data being used in each task, causing the results to slightly vary.
TASK 4: FORENSIC INVESTIGATION
Rule: y = 2.161x + 50.528
Predicted height= 171.544
The predicted height was calculated by using the equation that was found earlier. (Y) was the predicted height and (x) was the head circumference. The measurement for head circumference (56cm) was substituted into the equation (y=2.161x+50.528) and therefore predicting what the height would have been.