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

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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

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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.