INTRODUCTION TO ECONOMICS
In this module, your readings will focus on some of the major
principles and themes of microeconomics. Economics can be
defined as the study of the allocation of scarce resources among
competing uses. In this module, you are requ
Quartiles:
If we want to consider the raw data then our first step will be to arrange the data in
ascending order of magnitude, then:
The median is the middle value of the data set.
The lower quartile (Q1) is the first quartile of the data set.
The upper
Example:
Class
Frequency
Cumulative Frequency
0 up to 5
2
2
5 up to 10
7
9
10 up to 15
12
21
15 up to 20
6
27
20 up to 25
3
30
n/2 = 30/2 = 15, see the Cf column 15 lies on 21 (means 21>15) and see the lower class
in front of 21 i.e. 10, hence
Median for
Example:
The following table shows the downtime, in hours, recorded for 30 machines owned by a
large manufacturing company.
The period of time covered was the same for all machines.
4
6
1
8
1
4
10
6
4
4
1
5
10
3
4
4
5
1
9
11
1
8
13
4
8
4
2
5
9
9
Sol:
The
Firstly you click the TDB link you will see the following page.
Then click the My Topics link Under discussion Topics as highlighted in above picture
and you will see the Date and Time schedule of TDB assigned to you, as highlighted in
below picture.
Find the median, first and third quartile for the following frequency distribution.
Class Boundaries
145 150
150 155
155 160
160 165
165 170
170 175
h
n
Median = l +  C
f
2
Frequency
4
6
28
58
64
30
Class Boundaries
Frequency
Cumulative Frequency
145 1
The value of z statistics in 95% confidence interval is given as:
100(1 a )% = 95%
1 a = 0.95
a = 1  0.95
a = 0.05
a
0.05
=
2
2
a
= 0.025
2
Z score Chart
Negative zscores:
z
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.0
3.4
0.0002
0.0003
0.0003
0.
Lecture 24, Last Example, Part (a)
f(x) = kx.for 0<x<2
f(x) = 0 elsewhere
Find the value of K, if the given function is a density function.
SOLUTION:
We know that condition of the density function is that
+
f ( x) dx =1

According to the given question,
CS301 Data Structures Lecture No. 45 _
Data Structures Lecture No. 45
Reading Material
Data Structures and Algorithm Analysis in C+ 7.7 Chapter. 7.6, 7
Summary
Divide and Conquer Mergesort mergeArrays Mergesort and Linked Lists Mergesort Analysis Quickso
Hypergeometric Experiment:
There are four properties of Hypergeometric Experiment:
1. The outcomes of each trial may be classified into one of two categories, success and
failure.
2. The probability of success changes from trial to trial.
3. The trials ar
6 x y
where 0<x<2 and 2<y<4, then we want to
8
integrate this function with respect to x and y.
2 4
1
f ( x, y )dydx =  x  y )dydx
(6
80
x y
2
If we have the function f(x,y) =
In double integration, usually we have two variables and we integrate the s
Poisson process:
You should read the concept of Poisson process on book and understand it with the help
of this example.
Example
Flaws in plywood occur at random with an average of one flaw per 50 square feet. What
is the probability that a 32 square feet
INTRODUCTION TO ECONOMICS
Choosing a Firm
In this SLP assignment for this session, you will be asked to
examine the decisions of a small business owner. Since
microeconomics is the study of individual households, firms, and
government, we will take a clos
Example:
The names of 5 men and 5 women are written on slips of paper and place in a hat. Four names
are drawn. What is the probability that 2 are men and 2 are women?
Solution:
N = Number of units in the population = 5 men + 5 women = 10
n = Number of un
How to make Class limits and Class boundaries:
Let suppose an example to learn the concept of making the Class limits and Class
boundaries.
For a sample of 40 pizza products, the following data represent cost of a slice in dollars (S
Cost).
Product
S Cost
Dear student:
Its nice to see that you are learning at a fast pace. It shows your deep interest in this
subject. The medium of the course is English. MDB in Urdu or Roman languages will not
be accepted. So try to write in English.
There are mainly four qu
Find first quartile from the following data:
Class
Frequency
0 up to 5
2
5 up to 10
7
10 up to 15
12
15 up to 20
6
20 up to 25
3
Sol:
Class
Frequency
Cumulative Frequency
0 up to 5
5 up to 10
10 up to 15
15 up to 20
20 up to 25
2
7
12
6
3
2
9
21
27
30
h
n
Equally Likely:
Probability is the chance of something happening. Probability describes whether an
event is likely to happen, unlikely to happen, certain to happen, impossible, or more
likely, equally likely, or less likely to happen than another event.
I
Any function of a random variable X is also a random variable.
For example, H(X) is a function of X (and X is a random variable) then H(X) is also a
random variable.
Also kth moments about mean of a random variable X are calculated as:
m k =E ( X  m )
=