Mean and standard deviation

edited August 13 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 13

    %%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 13

    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 13

    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 13

    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%%

  • edited August 13

    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 13

    %%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 13

    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 13

    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

  • edited August 14

    %%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.%%

  • edited August 12

    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.

  • edited August 13

    %%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 2

    %%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 13

    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 13

    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 13

    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 13

    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 13

    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 23

    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%%

  • edited August 13

    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 13

    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 13

    %%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.%%

  • 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 14

    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 14

    %%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 14

    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 14

    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 14

    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
Sign In or Register to comment.