Math 132A

Summaries of Numerical Variables 1

Name Major College Color Height Siblings Section
Arabella Nursing HHS Green 66 5 02
Raily Occupational Therapy HHS Pink 73 2 02
Hailey Undecided HHS Pink 61 2 02
Sydney Nursing HHS Pink 63 1 02
Madolyn Criminal Justice ABS Purple 65 5 02
Johanna Occupational Therapy HHS Purple 65 2 02
Taylor Nursing HHS Pink 64 2 02
Kaylee Medical Lab Science HHS Pink 61 2 02
Akzhuurat Pre-Nursing HHS Purple 63 3 02
Glorie Music Education COE Purple 64 3 02
Elise Nursing HHS Blue 62 2 02
Marlene Exercisee Science HHS Purple 69 1 02
Hosanna Elementary Education COE Green 65 1 02
Lala Nursing HHS Pink 63 2 02
Amelia Nursing HHS Green 68 5 02
Ashley Nursing HHS Blue 65 2 02
Ryder Criminal Justice ABS Blue 78 1 02
Pjetra Computer Science SET Pink 66 1 02
Alyssa Nursing HHS Pink 64 2 02
Kaitlin Nursing HHS Pink 64 2 02
Xavier Social Studies ABS Burgundy 71 1 02
David Public Health HHS Blue 67 3 02
Sydney Nursing HHS Green 68 1 02
Mercades Occupational Therapy HHS Pink 62 3 02
Kaleigh Nursing HHS Blue 65 2 02
Drew Elementary Education COE Yellow 65 2 02

Collected Variables

Rows: 26
Columns: 7
$ Name     <chr> "Arabella", "Raily", "Hailey", "Sydney", "Madolyn", "Johanna"…
$ Major    <chr> "Nursing", "Occupational Therapy", "Undecided", "Nursing", "C…
$ College  <fct> HHS, HHS, HHS, HHS, ABS, HHS, HHS, HHS, HHS, COE, HHS, HHS, C…
$ Color    <chr> "Green", "Pink", "Pink", "Pink", "Purple", "Purple", "Pink", …
$ Height   <dbl> 66, 73, 61, 63, 65, 65, 64, 61, 63, 64, 62, 69, 65, 63, 68, 6…
$ Siblings <int> 5, 2, 2, 1, 5, 2, 2, 2, 3, 3, 2, 1, 1, 2, 5, 2, 1, 1, 2, 2, 1…
$ Section  <chr> "02", "02", "02", "02", "02", "02", "02", "02", "02", "02", "…
  • <chr>: “character”
  • <fct>: factor
  • <ord>: ordered factor
  • <dbl>: “double”
  • <int>: integer

Categorical Variables

  • Frequency Table
Color Freq
Blue 5
Burgundy 1
Green 4
Pink 10
Purple 5
Yellow 1
  • Bar Graph

… (another option)

  • Relative Frequency Table
Color Freq (%)
Blue 19.23
Burgundy 3.85
Green 15.38
Pink 38.46
Purple 19.23
Yellow 3.85
  • Relative Bar Graph

A Factor

  • Frequency Table
College Freq
ABS 3
BUS 0
COE 3
HHS 19
SET 1
  • Bar Graph

Discrete Numerical Variable

  • Frequency Table
Siblings Freq
1 7
2 12
3 4
5 3
  • 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
61 63.25 65 66.75 78 65.65385 3.815152 26 0

Box-plot

min Q1 median Q3 max mean sd n missing
61 63.25 65 66.75 78 65.65385 3.815152 26 0

Box-plot

min Q1 median Q3 max mean sd n missing
61 63.25 65 66.75 78 65.65385 3.815152 26 0

Mean

66 73 61 63 65 65 64 61 63 64 62 69 65 63 68 65 78 66 64 64 71 67 68 62 65 65

Standard Deviation

61626364656667686970717273747576777865.6538471−65.6538462−65.6538478−65.6538461−65.65384deviation:𝑥−𝑥=71−65.65384=5.34616deviation:𝑥−𝑥=62−65.65384=−3.65384deviation:𝑥−𝑥=78−65.65384=12.34616deviation:𝑥−𝑥=61−65.65384=−4.65384variance=”mean”ofsquaresofallthedeviationsvariance=1𝑛−1∑(𝑥−𝑥)2standarddeviation:𝑠=√variance

\(x\) \(x - \overline{x}\) \((x - \overline{x})^2\)
66 0.35 0.1225
73 7.35 54.0225
61 -4.65 21.6225
63 -2.65 7.0225
65 -0.65 0.4225
65 -0.65 0.4225
64 -1.65 2.7225
61 -4.65 21.6225
63 -2.65 7.0225
64 -1.65 2.7225
62 -3.65 13.3225
69 3.35 11.2225
65 -0.65 0.4225
63 -2.65 7.0225
68 2.35 5.5225
65 -0.65 0.4225
78 12.35 152.5225
66 0.35 0.1225
64 -1.65 2.7225
64 -1.65 2.7225
71 5.35 28.6225
67 1.35 1.8225
68 2.35 5.5225
62 -3.65 13.3225
65 -0.65 0.4225
65 -0.65 0.4225
1707 363.885

\(\displaystyle\overline{x} = \frac{1707}{26} = 65.65\)

  • Sum of square deviations: \[\sum (x - \overline{x})^2 = 363.885\]
  • Variance: \[\frac{1}{25}\sum (x - \overline{x})^2 = \frac{363.885}{25} = 14.5553846\]
  • Standard Deviation: \[\sqrt{\frac{1}{25}\sum (x - \overline{x})^2} = \sqrt{14.5553846} = 3.815152\]

In R

favstats(~Height, data = classdata)
 min    Q1 median    Q3 max     mean       sd  n missing
  61 63.25     65 66.75  78 65.65385 3.815152 26       0
IQR(~Height, data = classdata)
[1] 3.5
median(~Height, data = classdata)
[1] 65
mean(~Height, data = classdata)
[1] 65.65385
sd(~Height, data = classdata)
[1] 3.815152