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7/31/2019 Stats Phase I
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Stats 1510 Research Project:
On the Relationship Between the Diameter and Circumference of Circular Objects
Ashlan Napier
Taft College
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face of the circular object. The space between these marks was measured with a ruler
to record the diameter of the object as pictured below.
The same general process was used to measure the circumference of the circular
object. The only difference being that the string was wrapped around the body of the
object like so:
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Again, the tape was only used for photographing purposes. After the string was marked
on the places it overlapped, the space between the two marks was measured as before.
This technique was used by an online college statistics class to measure the
circumference and diameter of 392 objects. Once the data was collected by the
students, it was submitted to the moodle website where the professor compiled the
information onto a spreadsheet. The data associated with 25 objects was randomly
selected using a TI84 calculators randInt application (randInt->0,392, 25), and recorded
in the following table. Also recorded was the Pi (circumference/diameter) of each object.
Table 1
Experimental Data
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Item # Object Circumference
Diameter Pi
1 Cup 262 82.5 3.1758
2 Mason Jar Lid 8.75 2.5 3.5
3 Green Ball 6.2 1.6 3.875
4 Quarter 3.375 0.938 3.5981
5 Clock Face 73 23.1 3.1602
6 Baseball 30 6 5
7 CampbellsSoup
8.5 2.625 3.2381
8 Vase 19.25 6 3.2083
9 Blue Bowl 11.5 5.75 2
10 CD 18 4.75 3.7895
11 Toilet PaperRoll
27.946 2.55 10.959
12 Yo-Yo 8 2.8 2.8571
13 Drum 37.75 12.125 3.113414 Tuna Can 10.625 3.375 3.1481
15 Trash Can 27.5 8.75 3.1429
16 Poker Chip 122.5 39 3.141
17 AA Battery 43.8 14 3.1286
18 Corn Tortilla 45.7 14 3.2643
19 Ping Pong Ball 5 2 2.5
20 Canned Peas 9.25 3 3.0833
21 PX Bottle 4.25 1.25 3.4
22 Wall Clock 31.5 9 3.5
23 Ranch Beans 283 88.9 3.1834
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Item # Object Circumference
Diameter Pi
24 Mirror 44.4 36.25 1.2248
25 Stove Knob 2.5 1 2.5
This data can be assumed to be representative of the population (the other objects
measured by the students), because it was obtained through the randomizing features
of the TI-84 calculator, which possesses no capacity for bias or human error. Using 1-
VarStats on the columns consisting of the measurements for Circumference, Diameter,
and Pi, the following data was calculated.
Table 2
Statistics Related to the Circumference, Diameter, and Pi Calculation.
Mean Median Standard
Deviatio
n
Q1 Q3 Min. Max.
Circumference
Diameter
Pi
47.184 19.25 73.2751 8.25 44.1 2.5 283
14.9505 5.75 23.6046 2.525 14 0.938 88.9
3.4676 3.1758 1.6995 3.0984 3.5 1.2248 10.9592
Although the statistics pertaining to both the circumference and the diameter of the data
fluctuates drastically, those related to Pi (circumference/diameter) stay relatively
constant. The mean and median of the Pi data are within tenths of each other,
suggesting that the data is normal. The standard deviation from the mean is also quite
small, suggesting that the relationship between the circumference and the diameter of
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each object holds fairly constant as well. All of these qualities can be illustrated by the
box and whisker plot found below.
Figure 1.
Pi Statistics Box and Whisker Plot
Upon examination of these statistics, it is reasonable to conclude that there is a definite
relationship between the circumference of a curved geometrical figure and its diameter.
This relationship can be found in the form of pi, a number approximating to about 3.14,
however, the data shown above has a slightly higher median value of 3.18, which could
easily be the result of human error in the measurement process. For example, the
students might have improperly recorded the results of either their circumference or
diameter measurement, or even measured incorrectly.
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Index
Table 4.
Data Collected by Professor Jean
Number Object Measur Circumference Diameter Describe the M
1 Quarter 3.375 0.938
2 Nickel 3.125 0.875
3 Dime 2.5 6.88
4 Golf Ball 5.375 1.625
5 Progresso Sou 11.25 3.375
6 Pepsi 12 oz can 8.875 3.625
7 Can of almonds 10.75 3.25
8 WD 40 8 oz can 8.5 2.625
9 Water bottle 11.25 3.5
10 Campbells sou 8.5 2.625
11 Quarter coin 7.5 2.4
12 Nickel coin 6.6 2.1
13 Dime coin 5.5 1.7
14 Tennis ball 19.6 6.5
15 Garbanzo bean 23.2 7.3
16 Coca-Cola can 20.6 6.5
17 Disposable plat 80.1 25.5
18 Corn tortilla 45.7 1419 CD 27 11.7
20 Disposable cup 30.7 9.8
21 Rice cooker 55.9 27.7
22 Trumpet's bell 39 12.2
23 Stand-alone fan 183.3 44.8
24 clock face 73 23.1
25 Clock 73 23.1
26 Quarter 3 1
27 Nickel 2.625 0.875
28 Dime 2.125 0.75
29 Ping Pong Ball 5 2
30 Refried beans 9 3
31 Dr. Pepper can 8.5 2.75
32 CD 16 5.5
33 Hairspray can 6.25 2
34 Beer cap (twist- 3.75 1
35 Sice C battery 3.25 1
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36 Vase 19 1/4 6
37 Blue Bowl 11.5 5.75
38 Quarter 2 0.75
39 Nickel 1.875 0.75
40 Dime 1.5 0.5
41 Canned peas 9.25 342 BaseBall 30 6
43 Soda can 8.5 4.25
44 wallet 48.5 28.5
45 Money jar 34 2.5
46 TC mug 10.5 8
47 Mug 11.7 3.5
48 Candle 13.9 5.4
49 water bottle 9.15 2.75
50 shaving cream 6.7 2.05
51 quarter 2.9 0.95
52 nickel 2.65 0.8
53 dime 2.25 0.7
54 baseball 8.9 2.65
55 Quarter 3.2 0.9
56 Del Monte pea 9.35 2.85
57 Nickel 2.6 0.8
58 Dime 2.1 0.7
59 Tennis Ball 19.8 6.5
60 soda can 6.6 2.05
61 Carnation Milk 9.3 2.9
62 Coke Can 8.3 263 penny 2.4 0.7
64 cd 15 4.7
65 Nescafe Jar 10.3 3.3
66 Small saucepan 15.1 5.2
67 Quarter 3.1 0.9
68 Nickel 2.8 0.8
69 Dime 2.1 0.75
70 Baby Ball 8 3.4
71 Gravy Can 8.6 2.8
72 Soda Can 8.3 2.9
73 Bottle of Wine 10.5 3.3
74 Vitamin Bottle 7.6 2.3
75 Candle 4 3.3
76 Face cream jar 7.3 2.4
77 Hair spray bottl 7.2 2.3
78 Salt shaker 5.8 1.7
79 Quarter 8 2.4
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80 Nickel 7.1 2.1
81 Dime 5.9 1.7
82 Baseball 22.5 6.4
83 Can of Sliced P 23.6 7.4
84 Sliced Peaches 23.6 7.4
85 Soda Can 20.8 6.186 0.15 oz Lip Bal 5.2 1.5
87 Nail Polish Bottl 8.3 2.5
88 Makeup Contai 16.9 5.1
89 Compact-Make 22.9 7.2
90 Quarter 3.25 0.9375
91 Nickel 2.5 0.875
92 Dime 2.25 0.6875
93 Tennis Ball 8.5 2.5
94 15 oz Can of C 9.5 2.9375
95 Soda Can 8 2.5
96 Chapstick 2 1.625
97 Hair Spray 6 1.875
98 Candle 9.25 2.875
99 Water Bottle 7.5 2.375
100 Spool of Threa 5 1.5
101 Bottle of Hot S 5.25 1.75
102 Quarter 2.5 7.85
103 Nickel 2 6.28
104 Dime 1.5 4.71
105 Golf Ball 2.5 7.85
106 Kidney Beans 20.42 6.5107 Soda Can 15.7 5
108 Nature's Made 17.28 5.5
109 Grand's Biscuit 22.31 7.1
110 Paper Towel Ro 13.19 4.2
111 Spray bottle 15.7 5
112 Powder supple 36.86 11.7
113 Sour cream 29.85 9.5
114 paper plate 50.27 16
115 Quarter 3 1.2
116 Nickel 2.5 0.75
117 Dime 2.25 0.9
118 Basketball 29.33 9.34
119 Can of Soup 10.5 3.25
120 Can of Diet Cok 8.25 2
121 Can of hairspra 6.5 2
122 candle 9.5 3
123 Chap Stick 2.25 0.5
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124 # 2 Pencil 1 0.25
125 Quarter 2.999 0.955
126 Nickel 2.622 0.835
127 Dime 2.214 0.705
128 Stress Ball 11.775 3.75
129 Banana Creme 10.598 3.375130 Soda Can 7.85 2.5
131 Candle 4.71 1.5
132 Sobe LIfe water 4.318 1.375
133 Fan 29.438 9.375
134 Vase 4.318 1.375
135 Quarter 3 1
136 Nickel 2.75 0.75
137 Dime 2 0.68
138 Tennis Ball 8 2.5
139 Tuna Can 10.25 3.25
140 Soda Can 8.5 3
141 Vehicle Steerin 27 14.5
142 Class cup 9 2.5
143 Axe Spray Can 6.5 2
144 Quarter 2.9 0.9
145 Nickel 2.6 0.8
146 Dime 2.2 0.7
147 Ball (softball) 37.7 12
148 Canned food (g 9 2.9
149 soda can (Pepsi 6.7 2.1
150 coaster 11.8 3.8151 candle 11.8 3.8
152 Pill bottle 4.7 1.5
153 Ring 2.6 0.9
154 Quarter 3.1 1
155 Nickel 2.6 0.8
156 Dime 2.2 0.7
157 Baseball 9 2.9
158 Rosarita's Cann 9.25 3
159 Regular RiteAid 2 0.59375
160 8 oz. plastic, no 7.25 2.5
161 Drink coaster 12.75 4
162 CD 15 4.75
163 Soda Can 8.25 2.8
164 Quarter 78 24.8
165 Nickel 60 19.1
166 Dime 56 17.83
167 Basketball 1730 550.68
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168 Ranch Beans 283 88.9
169 Soda can 361 115
170 Tall Lamp 182 57.93
171 40 Oz Cup 780 24.28
172 Water bottle 375 119.37
173 Vault Handle 103 32.79174 Trophy Top 738 234.91
175 Quarter 1 3
176 Minature Socce 18 9
177 15oz Canned F 9 3
178 Soda Can 8 2.5
179 Wall Clock 31.5 9
180 Tall plastic cup 9.5 3.5
181 Large Metal Bo 25 8.25
182 Large Metal Pot 30 10
183 quarter 3.25 1
184 nickel 2.875 1.125
185 dime 2.25 1
186 childs bouncy b 9.5 3
187 15oz canned pr 9.5 3
188 soda can 8.5 2.75
189 penny 2.5 0.75
190 pill bottle 6 1.75
191 chapstick tube 2.125 0.825
192 dinner candle Feb 15, 2016 1
193 Stove Knob 2.5 2.5
194 Stove Knob 2.5 2.5195 Stove Knob 2.5 2.5
196 Stove Knob 2.5 2.5
197 Stove Knob 2.5 2.5
198 Canister 10.25 3.25
199 Salt Shaker 7 2.25
200 Candle Stick 3.5 2
201 Lamp Shade 22 6.5
202 Vase 4.5 4.5
203 PX Bottle 4.25 1.25
204 Camera Lens 1 1
205 Fan 30 30
206 Mirror 44.5 36.25
207 Curling Iron 2 2.5
208 Soda Can 8.375 2.125
209 Canned Food 9 2.75
210 Baseball 3.75 9
211 dime 0.75 2.5
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212 Nickel 2.88 0.76
213 Quarter 3.25 0.99
214 clock 120 16
215 plate 21.98 9
216 soda can (pepsi 8.188 2.62
217 Roll of Painters 12 2.5 I set the roll of t218 Candle 13 3 I set the candle
219 Orange 10 3 I set the orange
220 Fire Extinguish 14 4 I set the fire exti
221 Trash can 29 10 I set the trash c
222 Coffee Can 13 4 I set the coffee
223 Hot sauce bottl 8 2 I set the hot sau
224 Track ball 7 2 I set the track b
225 Door knob 7.5 2 I wrapped the c
226 soda can 9 2.5 I set the soda c
227 CD disc 392 121 Circumference:
Diameter: Use t
-record both
228 Partial roll of du 295 95 Circumference:
Diameter: use r
229 Small bike tire 652 208 Circumference:
Diameter: Use r
230 Poker Chip 122.5 39 Circumference:
Diameter: use a
231 Pocket Watch 136 43.5 Use the string t
use the ruler to
-record data in
232 AA Battery 43.8 14 Circumference:Diameter: use t
--record data in
233 Flashlight 178 57 Circumference:
Diameter: use t
234 cup 262 82.5 Circumference:
Diameter: use t
235 Spool (for threa 98 32 Circumference:
Diameter: use t
236 roll of toilet pap 394 125 Circumference:
Diameter: use t
237 Lid for protein s 14 4.125 I used a ruler to
238 Lid to vitamin b 5.875 1.5 I used a ruler to239 coaster 13.5 4.125 I used a ruler to
240 DVD 14.625 4.625 I used a ruler to
241 Candle 8.25 2.5 I used a ruler to
242 Plate 25.875 8.25 I used a ruler to
243 Lid to cookie tin 33.75 9.75 I used a ruler to
244 Lid to cooking 29.625 9.25 I used a ruler to
245 Flower pot 19.875 6.25 I used a ruler to
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246 Soufle Dish 11.25 3.5 I used a ruler to
247 Mason Jar lid 8.75 2.5 I used a ruler to
248 Empty duct tap 10.25 3 I used a ruler to
249 Ortiz 3.3 9.1 I used a ruler t
250 Pink ball 2.7 10.3 I used a ruler t
251 golf ball 5.1 1.5 I held the ruler252 Volley ball 51.5 7 I first measure
253 Green ball 6.2 1.6 I measured the
254 White ball 5.8 1.5 The first thing I
255 Blue/yellow ner 12.6 3.4 The ball was s
256 Blue ball 23.3 5.7 I measured firs
257 glass dish 9 5 I took the end o
258 wedding ring 3.25 0.9375 I took a tape m
259 Top of can of D 8.25 2.5 I put the tape m
260 top of maritini g 12.5 3.94 I put the tape m
261 homemade coff 15.75 5 I put the tape m
262 Mixing bowl 28.88 9.25 I put the tape m
263 bottom of 5 gall 34 10.875 I put the tape m
264 lid of an Isageni 6.88 2.13 I put the tape m
265 Crock Pot 33.88 10.75 I put the tape m
266 Base of Stand 39.5 12.5 I put the tape m
267 Marliyn Monroe 12.38 3.88 I put the tape m
268 Tall glass 14.758 2.35 I used a ruler an
269 pill bottle 8.1875 2.5 I grabbed a srti
270 Tapatio Bottle 0.9167 3.5625 I grabbed a srti
271 Soda Can 8.25 2.625 I grabbed a srti
272 Bottle of Lotion 5.9375 1.875 I grabbed a srti273 Little Pot 0.8333 3.5 I grabbed a srti
274 Marker 2.25 0.5 I grabbed a srti
275 Lamp 8.375 2.75 I grabbed a srti
276 White Out Bottl 0.3333 1.1875 I grabbed a srti
Cup 7.1875 2.125 I grabbed a srti
Jar 12.125 3.5625 I grabbed a srti
Small Bottle 8.625 2.625 I used a string t
Medium Bottle 10 3.25 I used a string t
Large Bottle 13.5 3.75 I used a string t
Paper Towel Ro 18.75 5.75 I used a string t
Large Candle 12.5 4 I used a string t
Empty Paper T 4.5 1.5 I used a string t
DVD 14.625 4.625 I used a string t
Tiny Pot 15.25 4.875 I used a string t
Medium Pot 25 7.75 I used a string t
Large Pot 30 9.375 I used a string t
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coffee bean pot 17.2 5.15 I used a ruler to
Coffee Bean po 17.2 5.15 I used a ruler to
Soda can base 6 1.95 I used a ruler to
wine bottle bas 9.25 2.8 I used a ruler to
beer bottle bas 8 2.1 I used a ruler to
clear wipes top 9.25 2.8 I used a ruler toair freshener ba 6.5 2 I used a ruler to
shaving cream 6.5 2 I used a ruler to
candle jar base 12.8 3.8 I used a ruler to
margarin jar ba 13 4.95 I used a ruler to
peanut butter ja 16.5 4 I used a ruler to
Jar of Glitter 9.2 2.6 I used a ruler to
Can of cake fro 10.7 3.5 Used a ruler to
Kirkland coffee 19.7 6.1 I measured the
Bottle of Ciroc 9.7 3 I used a ruler to
Lid of Vitamin c 7 2.4 I measured the
Lid of pill bottle 4.7 1.5 I used a piece o
Container of bl 16.2 5 I used string to
bottle body spr 7 2 wrapped cord a
can dog food 9.5 3 wrapped cord a
Lemonade Cani 16.5 5.5 wrapped cord a
round cheese 14.25 4.25 wrapped cord a
lamp base 18.5 6 used a measuri
1 gallon can of 21 6.5 measuring tape
1 gallon can of 21 6.5 measuring tape
1 gallon can of 21 6.5 measuring tape
spool of thread 10.5 3.1875 measuring tapespray can 21 7 measuring tape
drinking glass 29 9 measuring tape
barrel of monke 22 6.8 measuring tape
can of soups lid 8 2.5 I measured the
Can of tomato 11.2 3.5 I used a ruler to
Plastic Tea cont 14.5 4.5 I used a piece o
Magnet Plate 18.06 5.75 I set the plate d
Hat 23.6 7.5 I place the hat
Remote Control 13.2 4.2 I measured fro
Fire detector 18.8 6 Measured it as i
Video Game Di 14.8 4.7 Placed it on a s
Basketball 30.1 9.6 I found the dia
Baseball 8.75 2.79 Found the circu
Hockey Puck 9.1 2.9 Placed the puc
Paintball hoppe 9.7 3.1 Measured the it
Water bottle ca 3.61 1.15 Measured dow
Bowl 19.782 3.15 I used a ruler an
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Bangle 14.758 2.35 I measured the l
Candle 8.164 1.3 I took an unuse
Bottle cap 5.966 0.95 I Took a bottle
Pin 18.212 2.9 I took a pin with
Hat Box 38 12 I took my meas
stool 39 12 I took my meascandle lid 9.5 3 I took my meas
Bushes Baked 10.5 3.25 I took my meas
medium sized p 13 5 I took my meas
coat rack 49 15 I took my meas
Orange 8.4 2.6 Wrapped the th
Toy caterpillar 57.125 18 I took my meas
fan 63.125 21 I took my meas
CD 15.1 4.6 Put CD on ruler
cantaloupe 22 10.375 I took my meas
Tennis Ball 7.6 2.4 Wrapped string
paper plate 27 8.5 I took my meas
Marble 2.7 0.7 Wrapped sting
Rubber Ball 7.5 2.4 Wrapped the st
Quarter 2.8 0.8 Wrapped the st
Livestrong Ban 8.3 2.6 Wrapped the st
Penny 2.4 0.6 Wrapped the st
Plastic Cup 8.1 2.7 Wrapped the st
Can 8 2.5 Wrapped the st
Paper Towel Ro 15 4.75 First, I measure
Clock 34.5 11 First, I measure
Drum 37.75 12.125 First, I measureDrum 33 10.5 First, I measure
Dresser Drawer 5.2 1.6 First, I measure
Dresser Drawer 5.2 1.6 First, I measure
Trash Can 27.5 8.75 First, I measure
Water Bottle 8.5 2.625 First, I measure
Peanut Butter J 11.75 3.75 First, I measure
Paper Plate 28.5 9 First, I measure
Coffee Jar (Folg 19.5 6.25 First, I measure
Cd 29.83 4.75 I found a cd an
Sunglasses 15.7 2.5 I took a pair of
Compact powd 16.014 2.55 I measured it wi
Toilet paper roll 27.946 4.45 I got a full pape
Candle in Glass 13 4.25 To measure this
Playskool Sit 'N 23.25 7.25 To measure the
Febreeze Canis 7.5 2.375 To determine th
Bottle of Baby 6.875 2 To determine th
Tea Light Candl 5 1.5 To determine th
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Glass Cup 8.75 2.75 To determine th
Half of a Banan 4.625 1.375 To determine th
Peanut Butter J 11.625 3.625 To determine th
Wine Bottle Ba 9.5 3 To determine th
Tuna Can 10.625 3.375 To determine th
Bottom of a dri 7.5 2.4 Circumference:Diameter: I mea
YO-YO 8 2.8 Circumference:
Diameter: I mea
Life water bottl 5 1.5 Circumference:
Diameter: I mea
Bracelet 9 2.75 Circumference:
Diameter: I mea
Ben and Jerry's 12 3.75 Circumference:
Diameter: I mea
Auto-dri dog ea 4 1.25 Circumference:
Diameter: I mea
Beeman crow 8.5 3 Circumference:
Diameter: I mea
Men's aftersha 6 1.75 Circumference:
Diameter: I mea
Folders coffee li 12.5 4 Circumference:
Diameter: I mea
CD 18 4.75 Circumference:
Diameter: I mea
Stats 1510 Research Project! 17