Math 132A

Summaries of Numerical Variables

Name Major College Color Height Siblings Section
Layla Occupational Therapy HHS Pink 61 5 07
Natalie Occupational Therapy HHS Orange 65 1 07
Kelsey Medical Lab Science HHS Pink 62 5 07
Joe Exercisee Science HHS Blue 74 1 07
Charlotte Elementary Education NA Pink 66 6 07
Karma Occupational Therapy HHS Light Yellow 67 4 07
Olivia Cis SET Crimson 60 2 07
Moustafa Exercisee Science HHS Red 73 2 07
Olivia Bio SET Pink 66 1 07
Cole Exercisee Science HHS Blue 72 3 07
Owen Occupational Therapy HHS Blue 76 2 07
Kenadie Pre-Nursing HHS Yellow 66 4 07
Sarah Nursing HHS Pink 63 2 07
Nora Nursing HHS Blue 64 2 07
Piper Exercisee Science HHS Red 68 3 07
Emma Health Sciences HHS Navy 72 2 07
Moises Computer Science SET Purple 72 3 07
Olivia Pre-Nursing HHS Pink 63 3 07
Maddy Sec. Ed. Social Studies NA Teal 66 4 07
Erin Exercisee Science HHS Green 63 3 07
Kaitlin Exercisee Science HHS Green 65 4 07
Cynthia Elementary Education NA Pink 63 4 07
Bella Nursing HHS Pink 62 4 07
Lily Exercisee Science HHS Yellow 65 1 07
Savannah Occupational Therapy HHS Blue 63 3 07

Collected Variables

Rows: 25
Columns: 7
$ Name     <chr> "Layla", "Natalie", "Kelsey", "Joe", "Charlotte", "Karma", "O…
$ Major    <chr> "Occupational Therapy", "Occupational Therapy", "Medical Lab …
$ College  <fct> HHS, HHS, HHS, HHS, NA, HHS, SET, HHS, SET, HHS, HHS, HHS, HH…
$ Color    <chr> "Pink", "Orange", "Pink", "Blue", "Pink", "Light Yellow", "Cr…
$ Height   <dbl> 61, 65, 62, 74, 66, 67, 60, 73, 66, 72, 76, 66, 63, 64, 68, 7…
$ Siblings <int> 5, 1, 5, 1, 6, 4, 2, 2, 1, 3, 2, 4, 2, 2, 3, 2, 3, 3, 4, 3, 4…
$ Section  <chr> "07", "07", "07", "07", "07", "07", "07", "07", "07", "07", "…
  • <chr>: “character”
  • <fct>: factor
  • <ord>: ordered factor
  • <dbl>: “double”
  • <int>: integer

Categorical Variables

  • Frequency Table
Color Freq
Blue 5
Crimson 1
Green 2
Light Yellow 1
Navy 1
Orange 1
Pink 8
Purple 1
Red 2
Teal 1
Yellow 2
  • Bar Graph

… (another option)

  • Relative Frequency Table
Color Freq (%)
Blue 20
Crimson 4
Green 8
Light Yellow 4
Navy 4
Orange 4
Pink 32
Purple 4
Red 8
Teal 4
Yellow 8
  • Relative Bar Graph

A Factor

  • Frequency Table
College Freq
ABS 0
Business 0
Education 0
HHS 19
SET 3
NA 3
  • Bar Graph

Discrete Numerical Variable

  • Frequency Table
Siblings Freq
1 4
2 6
3 6
4 6
5 2
6 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 63 65 68 76 66.28 4.420784 25 0

Box-plot

min Q1 median Q3 max mean sd n missing
60 63 65 68 76 66.28 4.420784 25 0

Box-plot

min Q1 median Q3 max mean sd n missing
60 63 65 68 76 66.28 4.420784 25 0

Standard Deviation

606162636465666768697071727374757666.2873−66.2863−66.2876−66.2860−66.28deviation:𝑥−𝑥=73−66.28=6.72deviation:𝑥−𝑥=63−66.28=−3.28deviation:𝑥−𝑥=76−66.28=9.72deviation:𝑥−𝑥=60−66.28=−6.28variance=”mean”ofsquaresofallthedeviationsvariance=1𝑛−1∑(𝑥−𝑥)2standarddeviation:𝑠=√variance

\(x\) \(x - \overline{x}\) \((x - \overline{x})^2\)
61 -5.28 27.8784
65 -1.28 1.6384
62 -4.28 18.3184
74 7.72 59.5984
66 -0.28 0.0784
67 0.72 0.5184
60 -6.28 39.4384
73 6.72 45.1584
66 -0.28 0.0784
72 5.72 32.7184
76 9.72 94.4784
66 -0.28 0.0784
63 -3.28 10.7584
64 -2.28 5.1984
68 1.72 2.9584
72 5.72 32.7184
72 5.72 32.7184
63 -3.28 10.7584
66 -0.28 0.0784
63 -3.28 10.7584
65 -1.28 1.6384
63 -3.28 10.7584
62 -4.28 18.3184
65 -1.28 1.6384
63 -3.28 10.7584
1657 469.04

\(\displaystyle\overline{x} = \frac{1657}{25} = 66.28\)

  • Sum of square deviations: \[\sum (x - \overline{x})^2 = 469.04\]
  • Variance: \[\frac{1}{24}\sum (x - \overline{x})^2 = \frac{469.04}{24} = 19.5433333\]
  • Standard Deviation: \[\sqrt{\frac{1}{24}\sum (x - \overline{x})^2} = \sqrt{19.5433333} = 4.4207842\]