An archive of Mark's Fall 2017 Intro Stat course.

# Computing mean and standard deviation

mark

Compute the mean and the standard deviation of the data set

1,2,4,9.
hgrober

Can you please explain how to compute the standard deviation of a list of numbers?

mark

@hgrober I sure hope someone answers this question! In the meantime, there is an explanation with example at the bottom of this page.

brifro

Mean: (1+2+4+9)/4=4 .

Standard Deviation:
The terms are

• (1-4)^2=(-3)^2=9 ,
• (2-4)^2=(-2)^2=4 ,
• (4-4)^2=0^2 = 0 , and
• (9-4)^2=5^2 = 25

So the numerator is:
9+4+0+25= 38

Thus,
s=\sqrt{38/3} \approx 3.56 .

Elena

Hey! so to compute the standard deviation you would first want to find the mean, and then from there you will plug in your date like this: (x-mean)^2 +(x-mean)^2… and continue. For example if the mean for this set is 4, then I would plug in my data like this: (1-4)^2+(2-4)^2+(4-4)^2+(9-4)^2=38. then you divide by n-1. so if since our sample data is 4, we would subtract the sum of the equation above (38) by 3 since were subtracting 4-1. that would leave us with 12.6 as our variance. from here you just find the square root of 12.6 and that answer will give you the standard deviation.
(sorry this is kind of long and basically gives it away but i dont know how to answer it better )

Elena

mean: 4
standard deviation: 3.6

chriz

Mean: (1+2+4+9)/4=4
m=4

Standard Deviation: (9+4+0+25)/3
variance=12.66
sd=3.55

miles
• Mean: 1 + 2 + 4 + 9 = 16
16/4 = 4

• Standard Deviation:
(1-4) = -3^2 = 9
(2-4) = -2^2 = 4
(4-4) = 0^2 = 0
(94) = 5^2 = 25

• Numerator:
9 + 4 + 0 + 25 = 38

• So, the standard deviation is:
s = √38/3 = 3.55

GetSwifty

1+2+4+9 = 16
16/4 = 4

Mean:

1. 1+2+4+9 = 16

2. 16/4 = 4

So, the mean is 4

Std. Deviation:

1. (1-4)^2 + (2-4)^2 + (4-4)^2 + (9-4)^2 = 38

2. √38/n-1 = √38/4-1 = √38/3 = 3.56

So, the std. deviation is 3.56

Yennie

Mean:

m = (1+2+4+9)/4 = 4

Standard Deviation:

n = 4 (number of value in the data set)

s^2 = ((1-4)^2 + (2-4)^2 + (4-4)^2 + (9-4)^2))/(n-1)

s^2 = (9 + 4 + 0 + 25) / 3

s^2 = 38/3

s= 3.559

vee
1,2,4,9
1+2+4+9= 16. 16/4 = 4
4= mean.


Take the mean and plug it into this nifty little equation -

√((a-4)² + (b-4)² + (c-4)² + (d-4)²) /n1


n1 in this case would be 3, and the variables are replaced with the given number set.
(1, 2, 4, 9)

√((1-4)² + (2-4)² + (4-4)² + (9-4)²) /3


neat, right?
now simplify that.

√((-3)² + (-2)² + (0)² + (5)²) /3
√((9 + 4 + 0 + 25)) /3
√(38/3)
√(12.666666667) = 3.559


Round to two decimal points and ya get 3.56!
So there ya have it folks the mean is 4 and the standard deviation is 3.56.

Dancerlikens

Mean= 1+2+4+9/4= 4
SD= (1-4)^2+(2-4)^2+(4-4)^2+(9-4)^2
=9+4+0+25
=38/3
12.6 (take square root)
SD=3.55

avavball13

mean: 4
Standard deviation: 3.6

xoxoaphrodite

mean is 4
Standard deviation is 3.55

Nathan89

1,2,4,9
mean:
(1 + 2 + 4 + 9)/4 = 4

standard deviation:
(1-4)^2 = 9
(2-4)^2 = 4
(4-4)^2 = 0
(9-4)^2 = 25

√((9+4+0+25)/3)

√(38/3) = 3.56

CubsW98

Mean = 4
SD = 9+4+0+25= 38/3= √12.6666= 3.56

elackey101

The mean of the data set is 4. (1+2+4+9=16. 16/4=4.)

1-4=-3. -3x-3= 9
2-4=-2. -2x-2=4
4-4=0. 0x0=0
9-4=5. 5x5=25

9+4+0+25=38

Square root of 38 is 6.16

4-1=3 (mean minus 1)

Divide SR by 3

SD is approximately 3.55

mxcecilia

mean: (1+2+4+9)/4 = 4

standard deviation: 3.55
(1-4) = -3^2 = 9
(2-4) = -2^2 = 4
(4-4) = 0^2 = 0
(94) = 5^2 = 25

9+4+0+25=38
square root of 38/3= 3.55

asiarenee5

mean= (1+2+4+9 )/ 4 =4

Standard deviation= (1-4)^2 + (2-4)^2+(4-4)^2+(9-4)^2= 38
then square root of 38/3 = 3.56