Mean and standard deviation
(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
This discussion has been closed.
Comments
%%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
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 %%
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%%
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%%
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%%
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.%%
%%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.%%
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.%%
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
%%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.%%
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.
%%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.%%
%%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.%%
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 %%
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%%
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%%
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%%
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%%
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%%
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%%
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%%
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.%%
%%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.%%
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%%
%%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.%%
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.%%
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.%%
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%%
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%%