Math 132B

Class 5

Name Class Major College Color Height Siblings Group
Lauren Sophomore Biological science STEM Red 5’0” 1 sibling Group 2
Olivia Sophomore Biological science STEM Red 5’5” 3 siblings Group 2
Lana Junior Environmental science STEM purple 5’3” 5 siblings Group 2
Jasmine Sophomore Kinesology STEM/Health Pink 5’10” 7 siblings Group 2
Amanda freshman Nursing HHS Pink 5’1 0 3
Ava freshman occupational therapy HHS green 5’6 3 3
Coyden freshman Environmental science SET blue 5’10 1 3
Riley Junior Exercis Science HHS Green 6’3 0 3
Julia nontraditional (Junior) med lab sciences HHS blue 5’10 6 3
Fatimah Freshman Neuroscience NA All colors 5’6 only child Group 4
Conor Freshmen Biology NA green 5’8 2 siblings Group 4
Elizabeth sophomore Psych NA Pink/Brown 5’5 5 sib (1 bio) Group 4
Nastia freshmen exercise science NA navy 5’5 1 sibling Group 4
Ethan freshman nursing science/medicane blue 5’7 2 1
Lincoln Sophomore biology science purple 5’9 1 1
Emma junior CMB science black 5’4 2 1
Name Class Major College Color Height Siblings Group
Lauren Sophomore Biological Science HHS Red 60 1 2
Olivia Sophomore Biological Science HHS Red 65 3 2
Lana Junior Environmental Science HHS Purple 63 5 2
Jasmine Sophomore Kinesiology HHS Pink 70 7 2
Amanda Freshperson Nursing HHS Pink 61 0 3
Ava Freshperson Occupational Therapy HHS Green 66 3 3
Coyden Freshperson Environmental Science SET Blue 70 1 3
Riley Junior Exercise Science HHS Green 75 0 3
Julia NA Medical Lab Science HHS Blue 70 6 3
Fatimah Freshperson Neuroscience HHS All Colors 66 0 4
Conor Freshperson Biological Science SET Green 68 2 4
Elizabeth Sophomore Psych ABS Pink/Brown 65 5 4
Nastia Freshperson Exercisee Science HHS Navy 65 1 4
Ethan Freshperson Nursing HHS Blue 67 2 1
Lincoln Sophomore Biological Science SET Purple 69 1 1
Emma Junior Cell Biology, Molecular Biology, and Biomedical Sciences SET Black 64 2 1

Collected Variables

Rows: 16
Columns: 8
$ Name     <chr> "Lauren", "Olivia", "Lana", "Jasmine", "Amanda", "Ava", "Coyd…
$ Class    <ord> Sophomore, Sophomore, Junior, Sophomore, Freshperson, Freshpe…
$ Major    <chr> "Biological Science", "Biological Science", "Environmental Sc…
$ College  <fct> HHS, HHS, HHS, HHS, HHS, HHS, SET, HHS, HHS, HHS, SET, ABS, H…
$ Color    <chr> "Red", "Red", "Purple", "Pink", "Pink", "Green", "Blue", "Gre…
$ Height   <dbl> 60, 65, 63, 70, 61, 66, 70, 75, 70, 66, 68, 65, 65, 67, 69, 64
$ Siblings <int> 1, 3, 5, 7, 0, 3, 1, 0, 6, 0, 2, 5, 1, 2, 1, 2
$ Group    <int> 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 1, 1, 1
  • <chr>: “character”
  • <fct>: factor
  • <ord>: ordered factor
  • <dbl>: “double”
  • <int>: integer

Categorical Variables

  • Frequency Table
Color Freq
All Colors 1
Black 1
Blue 3
Green 3
Navy 1
Pink 2
Pink/Brown 1
Purple 2
Red 2
  • Bar Graph

… (another option)

  • Relative Frequency Table
Color Freq (%)
All Colors 6.25
Black 6.25
Blue 18.75
Green 18.75
Navy 6.25
Pink 12.50
Pink/Brown 6.25
Purple 12.50
Red 12.50
  • Relative Bar Graph

A Factor

  • Frequency Table
College Freq
ABS 1
Business 0
Education 0
HHS 11
SET 4
  • Bar Graph

An Ordered Factor

  • Frequency Table
Class Freq
Freshperson 7
Sophomore 5
Junior 3
Senior 0
NA 1
  • Bar Graph

Discrete Numerical Variable

  • Frequency Table
Siblings Freq
0 3
1 4
2 3
3 2
5 2
6 1
7 1
  • Bar Graph

Continuous Numerical Variable

Bin width 1:

Bin width 3:

Bin width 2:

Bin width 4:

Numerical Summaries

min Q1 median Q3 max mean sd n missing
60 64.75 66 69.25 75 66.5 3.794733 16 0

Box-plot

min Q1 median Q3 max mean sd n missing
60 64.75 66 69.25 75 66.5 3.794733 16 0

Box-plot

min Q1 median Q3 max mean sd n missing
60 64.75 66 69.25 75 66.5 3.794733 16 0

Standard Deviation

6061626364656667686970717273747566.570−66.563−66.575−66.560−66.5deviation:𝑥−𝑥=70−66.5=3.5deviation:𝑥−𝑥=63−66.5=−3.5deviation:𝑥−𝑥=75−66.5=8.5deviation:𝑥−𝑥=60−66.5=−6.5variance=”mean”ofsquaresofallthedeviationsvariance=1𝑛−1∑(𝑥−𝑥)2standarddeviation:𝑠=√variance

\(x\) \(x - \overline{x}\) \((x - \overline{x})^2\)
60 -6.5 42.25
65 -1.5 2.25
63 -3.5 12.25
70 3.5 12.25
61 -5.5 30.25
66 -0.5 0.25
70 3.5 12.25
75 8.5 72.25
70 3.5 12.25
66 -0.5 0.25
68 1.5 2.25
65 -1.5 2.25
65 -1.5 2.25
67 0.5 0.25
69 2.5 6.25
64 -2.5 6.25
1064 216

\(\displaystyle\overline{x} = \frac{1064}{16} = 66.5\)

  • Sum of square deviations: \[\sum (x - \overline{x})^2 = 216\]
  • Variance: \[\frac{1}{15}\sum (x - \overline{x})^2 = \frac{216}{15} = 14.4\]
  • Standard Deviation: \[\sqrt{\frac{1}{15}\sum (x - \overline{x})^2} = \sqrt{14.4} = 3.7947332\]