Download population variance

2.4 Stuff

The range of a data set is the difference between the
maximum and minimum data entries in the set.
2.4 Stuff

The deviation of an entry x in a population data set
is the difference between the entry and the mean 
of the data set.
Deviation of x = x – 
2.4 Stuff

The population variance of a population data set of
N entries is
( x   ) 2
Population variance =  
N
2

The population standard deviation of a population
data set of N entries is the square root of the
population variance.
2
Population standard deviation =   
2.4 Stuff

The sample variance and sample standard
deviation of a sample data set of n entries is
2

(
x

x
)
2
Sample variance = s 
n 1
Sample standard deviation = s 
s2
2.4 Exercise #13
The sample data set is
4 15 9 12 16
8 11 19 14
2.4 Exercise #33/35
The mean value of land and buildings per acre from a
sample of farms is $1,500, with a standard deviation
of $200. The data set has a bell-shaped distribution.
33) Estimate the percent of farms whose land and
building values per acre are between $1,300 and
$1,700.
35) If the sample size is 75, estimate the number of
farms whose land and building values per acre are
between $1,300 and $1,700.
2.4 Stuff

Chebychev’s Theorem. The portion of any data set
lying within k standard deviations (k > 1) of the mean is
at least
1
1 2
k


if k = 2, then 75% of the data lies within 2 standard
deviations
if k = 3, then it’s 88.9%.
2.4 Stuff

The sample standard deviation for a frequency
distribution is
( x  x ) 2 f
s
n 1
where n =  f is the number of entries.