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Paper Aeroplane Statistics

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by

Matt Drovandi

on 1 January 2015

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Transcript of Paper Aeroplane Statistics

Paper Airplane Experiment
The purpose of this assignment was to collect, display,
and analyse data on the flying
distances of different
paper airplane
models.

By interpreting the data,
conclusions were drawn on the flying efficiency of each of
the designs.

The Eagle Glider
Design 1:
Length: 20 centimeters
Wing span: 25 centimeters
Weight of model: 3.9 grams
Area of Wings: 225 square centimeters
This airplane model can be constructed from a standard A4 sheet of paper. This design also features a compact body with a widened nose, and tapered wing span.
Trial number Distance (cm)
1 456
2 489
3 523
4 556
5 423
6 361
7 513
8 672
9 532
10 498
11 487
12 533
13 587
14 446
15 587
16 511
17 456
18 469
19 503
20 512
Distance Data for the
Eagle Glider
To ensure consistency, each trial was conducted at the same height above ground level, and the distance was recorded where the nose of the model landed.
350≥-400
Twenty trials were conducted, and the distance traveled at each trial was recorded.
Distance Tally Frequency
350-400
400-450
450-500
500-550
550-600
600-650
650-700
1
2
6
7
3
0
1
7
6
5
4
3
2
1
Frequency Table and Histogram
Eagle Glider
400-450
450-500
500≥-550
550≥-600
600≥-650
650≥-700
Distance (cm)
Frequency
median = 507
By placing the
distance data into
suitably sized bins,
we can determine that
the modal class is
500-550 cm.
Descriptive Statistics for the Eagle Glider
= sum of all values
number of values
= 10074/20
= 503.7cm
= (n+1)/2
= (20+1)/2
= 21/2
= 10.5th position
= (503+511)/2
= 507cm
= max value - min value
= 672 - 321
= 351cm
mean
median position
median
range
Length: 15 centimeters
Diametre: 20 centimeters
Weight of model: 3.7 grams
Surface area: 170 square centimeters
Design 2:
The UFO
This model features a thin cylindrical design with a hollow center. Lift is created by the column of air that passes through the centre.
As with the previous data collection procedure, twenty trials were conducted using this model, and the distance traveled at each trial was recorded.
Trial number Distance (cm)
1 572
2 598
3 634
4 657
5 602
6 648
7 598
8 750
9 634
10 540
11 536
12 544
13 576
14 612
15 623
16 629
17 502
18 476
19 659
20 639
To ensure consistency, each trial was conducted at the same height above ground level, and the distance was recorded where the nose of the model landed.
Distance Data for The UFO
Descriptive Statistics for the
= sum of all values
number of values
= 12029/20
= 601.45cm
= (n+1)/2
= (20+1)/2
= 21/2
= 10.5th position
= (602+612)/2
= 607cm
= max value - min value
= 750 - 476
= 274cm
mean
median position
median
range
UFO
450≥-500
Distance Tally Frequency
450-500
500-550
550-600
600-650
650-700
700-750
750-800
1
4
4
8
2
0
1
7
6
5
4
3
2
1
Frequency Table and Histogram
500-550
550-600
600≥-650
650≥-700
700≥-750
750≥-800
Distance (cm)
Frequency
By placing the
distance data into
suitably sized bins,
we can determine that
the modal class is
600-650 cm.
8
The UFO
median = 607
Five Number
Summary:
Eagle Glider
361
423
446
456
456
469
487
489
498
503
511
512
513
523
532
533
556
587
587
672
507
532.5
462.5
First Quartile
Median
Third Quartile
Maximum
Minimum
Identifying outliers:
Q1 - 1.5 x IQR
Q3 + 1.5 x IQR
= 462.5 - 1.5 x (532.5 - 462.5)
= 462.5 - 105
= 357.5
= 532.5 + 1.5 x (532.5 - 462.5)
= 532.5 + 105
= 637.5
361
462.5
507
532.5
587
0
+
-
=
9
8
7
1
2
3
4
5
6
c
Five Number
Summary:
The UFO
476
502
536
540
544
572
576
598
598
602
612
623
629
634
634
639
648
657
659
750
607
636.5
558
First Quartile
Median
Third Quartile
Maximum
Minimum
Identifying outliers:
Q1 - 1.5 x IQR
Q3 + 1.5 x IQR
= 558 - 1.5 x (636.5 - 558)
= 558 - 117.75
= 440.25
= 636.5 + 1.5 x (636.5 - 558)
= 636.5 + 117.75
= 754.25
476
558
607
636.5
750
Box and whisker plots
350
400
450
500
550
600
650
700
750
Eagle Glider
The UFO
Distance (cm)
By comparing the box and whisker plots for both airplanes, it is clear that the UFO model is a more
efficient
design in terms of flying ability.
The
five number summary
for each data set can be used to build a
box and whisker plot
. The spacings between the different parts of the box help indicate the degree of
spread
and
skewness
in the data, and identify
outliers
.
The
UFO
design is the winner
The
Eagle Glider
design is the loser
When conducting the experiment, it was important to ensure that all other variables acting upon the flight of the airplanes remained the same for each model. However, during the trials, there was some inconsistency in the amount of force imparted, and angle of release, during each throw.
Flaws in conducting experiment
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