Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
1. Prove that
∑
i
=
1
n
(
x
i
−
μ
)
2
=
∑
i
=
1
n
(
x
i
2
)
−
n
μ
2
\sum_{i=1}^{n} (x_i - \mu)^2 = \sum_{i=1}^{n} (x_i^2) - n\mu^2
∑
i
=
1
n
(
x
i
−
μ
)
2
=
∑
i
=
1
n
(
x
i
2
)
−
n
μ
2
. 2. The data set
x
1
,
x
2
,
…
,
x
25
x_1, x_2, \dots, x_{25}
x
1
,
x
2
,
…
,
x
25
has
∑
i
=
1
25
x
i
2
=
2568.25
\sum_{i=1}^{25} x_i^2 = 2568.25
∑
i
=
1
25
x
i
2
=
2568.25
and population standard deviation 5.2. Find the mean of the data set.
Browse the problem library