Mean and standard deviation

edited August 2020 in Assignments

(10 pts)

Generate four numbers by taking the positions in the alphabet of the first four letters of your first name (append your last name, if necessary). For example, my name is "Mark" so my numbers are

$$13,1,18,11.$$

Compute the sample mean and standard deviation of that list of numbers - showing your work using AscIIMath input!


My solution would be

%%mu = (13+1+18+11)/4 = 10.75%%

and

%%sigma = sqrt(((13-10.75)^2 + (1-10.75)^2 + (18-10.75)^2 + (11-10.75)^2)/3) ~~ 7.13559.%%

Note that I am definitely hoping that you use the auto-typesetting facility built into the site. For example, to type my solution into the webpage, I typed:

My solution  would be

%%mu = (13+1+18+11)/4 = 10.75%%

and 

%%sigma = sqrt(((13-10.75)^2  + (1-10.75)^2 + (18-10.75)^2 + (11-10.75)^2)/3) ~~ 7.13559.%%

The general form here is called ASCIIMath and is quite simple but powerful

«1

Comments

  • edited August 2020

    %%μ= [10+1+14+5] / 4 = 7.5%%

    %%σ= √[(10-7.5)^2 + (1-7.5)^2 + (14-7.5)^2 + (5-7.5)^2] /3 %% ≈ 5.69

    mark
  • Brandon
    %%mu = (1+2+14+18)/4 = 8.75%%
    %% sigma = sqrt(((1-8.75)^2+(2-8.75)^2+(14-8.75)^2+(18-8.75)^2)/3) ~~ 8.54 %%

    mark
  • edited August 2020

    Patrick Dimond
    P,A,T,R

    %%mu = (16+1+20+18)/4 = 11%%

    %%sigma = sqrt(((16-11)^2 + (1-11)^2 + (20-11)^2 + (18-11)^2)/3) ~~ 12.85%%

    mark
  • edited August 2020

    Taylor
    20, 1, 25, 12, 15, 18

    %%μ = (20+1+25+12+15+18)/6=15.167%%
    %%σ =√((20-15.167)^2 + (1-15.167)^2 + (25-15.167)^2 + (12-15.167)^2+ (15-15.167)^2 + (18-15.167)^2) / 5 ≈ 8.23%%

    mark
  • edited August 2020

    Harry
    7, 1, 17, 17

    %%μ = (7+1+17+17) / 4 = 10.5%%

    %%σ = sqrt((7-10.5)^2 + (1-10.5)^2 + (17-10.5)^2 + (17-10.5)^2) / 3 ≈ 7.8952%%

    mark
  • edited August 2020

    Hailey

    8, 1, 9, 12, 5, and 25

    %%mu = (8 + 1 + 12 + 5 + 25)/6 = 10%%

    and

    %%sigma = sqrt(((8-10)^2 + (1-10)^2 + (9-10)^2 + (12-10)^2 + (5 - 10)^2 + (25 - 10)^2)/6 ~~ 7.53.%%

    mark
  • edited August 2020

    %%mu = (5+22+1+14)/4 = 10.5%%

    %%sigma = sqrt(((5-10.5)^2 + (22-10.5)^2 + (1-10.5)^2 + (14-10.5)^2)/3) ~~ 232.083.%%

    mark
  • edited August 2020

    My solution would be

    %%mu = (1+21+4+18)/4 = 11%%

    and

    %%sigma = sqrt(((1-11)^2 + (21-11)^2 + (4-11)^2 + (18-11)^2)/3) ~~ 9.97.%%

    mark
  • edited August 2020

    μ = 1 + 12 + 5 + 24 + 1 +53/ 5= 10.6
    σ = √(1-10.6)^2 + (12-10.6)^2 + (5-10.6)^2 + (34-10.6)^2 + (1-10.6)^2 / 4 ≈ 13.83

    mark
  • edited August 2020

    %%mu = (3+1+12+5)/4 = 5.25%%

    and

    %%sigma = sqrt(((1-5.25)^2 + (3-5.25)^2 + (5-5.25)^2 + (12-5.25)^2)/3) ~~ 4.79.%%

    mark
  • edited August 2020

    μ=20+15+13+7=13.75
    σ=√(20−13.75)2+(15−13.75)2+(13−13.75)2+(7−13.75)24≈4.69707.

    mark
  • edited August 2020

    %%mu = (23+1+4+5)/4 = 8.25%%

    %%sigma = sqrt(((23-8.25)^2 + (1-8.25)^2 + (18-8.25)^2 + (11-8.25)^2)/3) ~~ 9.979.%%

    mark
  • edited September 2020

    %%mu = (10+1+3+11)/4 = 6.25%%

    and

    %%sigma = sqrt(((10-6.25)^2 + (1-6.25)^2 + (3-6.25)^2 + (11-6.25)^2)/3) ~~ 7.13559.%%

    mark
  • edited August 2020

    Sims
    %%mu=(18+8+12+18)/4 = 14%%
    %%sigma = sqrt(((18-14)^2+(8-14)^2+(12-14)^2+(18-14)^2)/3) approx 4.90 %%

    mark
  • Leon -> 12,5,15,14

    %%mu = (12+5+15+14)/4 = 11.5%%

    %%sigma=sqrt(((12-11.5)^2+(5-11.5)^2+(15-11.5)^2+(14-11.5)^2)/3)~~ 4.50925%%

    mark
  • edited August 2020

    Amber
    %%mu=(1+13+2+5+18)/5=7.8%%

    and

    %%sigma=sqrt(((1-7.8)^2+(13-7.8)^2+(2-7.8)^2+(5-7.8)^2+(18-7.8)^2)/4)~~7.39594%%

    mark
  • edited August 2020

    Chris --> 3, 8, 18, 9

    %%μ = (3 + 8 + 18 + 9)/4 = 9.5%%

    %%σ = sqrt(((3-9.5)^2 + (8-9.5)^2 + (18-9.5)^2 + (9-9.5)^2)/3)≈6.244998%%

    mark
  • edited August 2020

    Albert- 1,12,2,5

    %%mu = (1+12+2+5)/4 = 5%%

    %%sigma = sqrt(((1-5)^2 + (12-5)^2 + (2-5)^2 + (5-5)^2)/3) ~~ 26.6%%

    mark
  • edited August 2020

    Conor-3,15,14,15

    %%mu = (3+15+14+15)/4 = 11.75%%

    %%sigma = sqrt ( ( (3-11.75)^2 + (15-11.75)^2 + (14-11.75)^2 + (15-11.75) ^2)/3) ~~ 5.852349955%%

    mark
  • edited August 2020

    Anjuli:

    1,14,10,21

    %%mu=(1+14+10+21)/4=11.5%%
    %%sigma = sqrt(((1-11.5)^2+(14-11.5)^2+(10-11.5)^2+(21-11.5)^2))/3=approx8.34%%

    mark
  • edited August 2020

    bella- 2, 5, 12, 12
    %%mu=(2+5+12+12)/4=7.75%%
    %%sigma=sqrt(((2-7.75)^2+(5-7.75)^2+(12-7.75)^2+(12-7.75)^2)/3)--5.058%%

    mark
  • edited August 2020

    Denley
    %%mu = (4+5+14+12)/4 = 8.75%%

    %%sigma = sqrt(((4-8.75)^2 + (5-8.75)^2 + (14-8.75)^2 + (12-8.75)^2)/3) ~~ 4.99.%%

    mark
  • edited August 2020

    %%mu = (4+13+13+1)/4 = 7.75%%

    %%sigma = sqrt(((4-7.75)^2 + (13-7.75)^2 + (13-7.75)^2 + (1-7.75)^2)/3) ~~ 6.18.%%

    mark
  • Laura
    %%mu = (12+1+21+18)/4 = 14%%
    and
    %%sigma = sqrt(((12-13)^2 + (1-13)^2 + (21-13)^2 + (18-13)^2)/3 ~~ 8.83176.%%

    mark
  • edited August 2020

    2,12,1,9

    %%mu=(2+12+1+9)/4=6%%

    and

    %%sigma=sqrt((2-6)^2+(12-6)^2+(1-6)^2+(9-6)^2)/3~~5.356%%

    mark
  • edited August 2020

    %%mu = (10+1+11+5)/4 = 6.75%%

    and

    %%sigma = sqrt(((10-6.75)^2 + (1-6.75)^2 + (11-6.75)^2 + (5-6.75)^2)/3) ~~ 4.645.%%

    mark
  • J, o, h, n = 10, 15, 8, 4

    %%mu = (10+15+8+4)/4 = 11.75%%

    %%sigma = sqrt(((10-11.75)^2 + (15-11.75)^2 + (8-11.75)^2 + (4-11.75)^2)/3) ~~ 3.304038.%%

    mark
  • edited August 2020

    g, r, a, c, e = 7,18,1,3,5

    %%mu = (7+18+1+3+5)/5 = 6.8%%

    %%sigma = sqrt(((7-6.8)^2 + (18-6.8)^2 + (1-6.8)^2 + (3-6.8)^2 + (5-6.8)^2)/4) ~~ 6.64831.%%

    mark
  • edited August 2020

    16, 9, 16, 5

    %%mu = (16+9+16+5)/4= 11.5%%

    %%sigma = sqrt(((16-11.5)^2 + (9-11.5)^2 + (16-11.5)^2 + (5-11.5)^2)/3) ~~ 5.4467115%%

    mark
  • edited August 2020

    my solution:

    19, 20, 5, 18

    %%mu = (19+20+5+18)/4 = 15.5%%

    and

    %%sigma = sqrt(((19-15.5)^2+(20-15.5)^2+(5-15.5)^2+(18-15.5)^2)/3) ~~ 7.047%%

    mark
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