19)
If the director's salary is doubled, and all other salaries
True
Can't Tell
False
remain the same, that increases the average salary.
20)
If the director's salary is doubled, and all other salaries
True
Can't Tell
False
remain the same, that increases the median salary.

21)

22)
A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it
has just been discovered that an observation which was erroneously recorded as "30" actually
had a value of "35". If we make this correction to the data, then:

23)
Consider a sample with
107
x
=
and n = 23. If I remove the scores 87, 103, and 99 from the
sample, what will the mean become?

24)
A dataset contains 100 measurements with 50th, 51st and 52nd smallest observations being 69, 71
and 73. The median of this dataset is
(a)
69
(b)
71
(c)
70
(d)
72
(e)
73
(f)
None of the above

26

27
Chapter 3: Correlation, Covariance and Portfolios
We
now know how to create summary statistical measures for single variables such as the mean
and variance. A data set that contains only one variable of interest, as we have been examining
so far, is called a univariate data set. Data sets that contain two variables of interest are said to be
bivariate. More than two variable data sets are simply called multivariate.
With bivariate data, which is of the form (
,
)
i
i
x
y
for say
n
pairs of data, a basic question of
interesting is if there is a relationship (association) between the two variables. There are two
measures we will now study called
covariance
and
correlation
. Both of these are measures of
linear association between two variables; covariance gives direction of association and
correlation gives direction and strength.
In the case of bivariate or multivariate data sets we are often interested in whether elements that
have high values of one of the variables also have high values of other variables. For example, as
we might be interested in whether people with more years of schooling earn higher incomes.
As a very simplistic (but real) example, we will examine the relationship between outside
temperature in Fahrenheit
and how many chirps a cricket makes in 15 seconds. It turns out that
as the temperature goes up, crickets chirp more and more. In fact, one can derive an approximate
formula for the current temperature by counting the number of chirps in 15 seconds as we will
see when we cover regression.
Here is a graph of some collected cricket data, and there does appear to be a relationship between
chirps and temperature.
50
60
70
80
Temp
10
20
30
40
50
Chirps

28
To formalize how to measure a relationship between two variables, suppose we randomly collect
n
pairs of data of the form (
,
)
i
i
x
y