Statistics I (STAT 2040) - Lecture Notes

STAT 2040 Notes




SUMMER
SEMESTER
OF 2020

, Descriptive Statistics
MEASURES OF CENTRAL TENDENCY

The sample mean I the ordinary
is
average
-




, ,



E Xi
↳
I = /n

middle value when data set ordered from smallest
largest
-


Median -
is the a is to

-
Mode -
is the most frequently occurring value


observations
Modal Class the class on a
histogram with the most
-

-




For skewed distributions the median
right mean >
-

-




For left skewed distributions the mean < median
-
-




For a perfectly symmetric distribution the mean median
-
=




The mean is more influenced by extreme observations
-




The median used as a descriptive measure
-

is


-


The mean is often used in statistical inference procedures

of the smallest and are removed before
largest observations
Trimmed Mean the mean
calculating
a certain
percentage
-
-




where different values
Weighted Mean weight
the calculation
-

are more in
given
-




MEASURES OF VARIABILITY

-

The deviation of a value from the mean is the value subtract the mean

-
A deviation is the distance from the mean

-

The sum of the deviations is always zero


Mean Absolute Deviation ( MAD) the distance from the
average mean
- -




El Xi I 1
↳ In
-



MAD =




( S2 ) distance from the mean
average squared
-



sample variance -

the
5)
↳
gz =
E ( Xi -




4h . I

-

The sample variance is used to estimate the population variance


standard Deviation the
square root of the variance
-
-




↳
s =
is = Min ,
The
larger the variance and standard deviation the the variability
greater
-




,




-

The empirical rule is used to estimate how many standard deviations a value is from the mean for a mound -
shaped

distribution

WHY DIVIDE BY N -
1?

-



sample mean and variance estimate the population mean 2nd variance

-
El Xi - *
Mn tends to underestimate the population variance


we lose one
degree of freedom when we estimate the population mean with the sample mean
-

, Z -
SCORES


An observation 's of how small that observation is relative to the other observations
2 score is a measure
large
-
-

or in


the data set

Xi
51g
-




z
-
.
=




An observation 's score tells us how many standard deviations that observation is above below the mean
-

2 -
or


-
Z -


scores are Uni Hess ,
have a mean of zero and a standard deviation of one

-


Empirical rule for mound shaped -

distributions

↳ 68% of I and I
scores lie between
~
z
-
-




↳ ~
95% of z scores lie between
-
-
22nd 2

↳ All or almost all 2 scores lie between
-
-
3 and 3