Stats Phase I

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

Stats 1510 Research Project! 1


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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



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



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


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