first lecture to elementary statistcs

Course Title: General Statistics
Course Code: Math 161T
Programs in (College of Sciences +College of Computer
Sciences and Information + College of business and
administration)
Course coordinator: Dr. Wafa Alfawzan
Associate Professor; Department of Mathematical
Sciences, College of Science, Princess Nourah bint
Abdulrahman University

1- Larson, R., Farber, B., Elementary Statistics-Picturing
the world, 5th Ed.
2- Walpole, R. E., Myers, R. H., and S. L. Myers (2007),
Probability and Statistics for Engineers and Scientists, 8th
ed., Prentice-Hall, inc., Upper Saddle River, new Jersey.
References

My Rules
•Listen Carefully
•Do not talk with your friend in class.
•Raise your hand for asking.
•Do not be late for lecture.

1)The definition of statistics.
2) How to distinguish between a population and a sample.
3) How to distinguish between qualitative data and quantitative data.
4) How to distinguish between descriptive statistics and inference
statistics.
5) How to construct a frequency distribution including limits,
midpoints, relative frequencies, Percentage frequency table,
cumulative frequency table.
WHAT YOU SHOULD
LEARN?

The reasons for the appearance of Statistics:
• Census community.
• Inventory of the wealth of individuals.
• Data on births, deaths and production and consumption.
Introduction to Statistics

Data consist of information coming from
observations, counts, measurement, or
responses. The singular for data is datum.
Definition of data

Statistics is the science of collecting, organizing,
analyzing, and interpreting data in order to make
decisions.
Definition statistics
There are two types of data sets you will use when studying
statistics. These data sets are called populations and samples.

A population In statistics,
population is the collection of all outcomes, responses,
measurements, or counts that are of interest. For
example, if we are studying the weight of adult
women, the population is the set of weights of all the
women in the world.
Definition of a population (p.g. 3 Larson and Farber)

A sample is a subset, or part, of a population. In
order to use statistics to learn things about the
population.
Definition of a sample (p.g. 3 Larson and
Farber)

1. bring the population to a manageable number
2. To reduce cost.
3. To help in minimizing error from the despondence
due to large number in the population.
4. Sampling helps the researcher to save time.
Reasons for drawing a sample, rather than
study a population

1. A parameter is a numerical description of a
population characteristic.
2. A statistic is a numerical description of a sample
characteristic.
Note: It is important to note that a sample statistic can
differ from sample to sample whereas a population
parameter is constant for a population.
Definition of a parameter and a
statistic (p.g. 4 Larson and Farber)

Descriptive statistics is the branch of statistics that
involves the organization, summarization , and display
of data.
Statistical inference is the branch of statistics that
involves using a sample to draw conclusions about a
population.
BRANCHES OF STATISTICS (p.g. 5
Larson and Farber)

Qualitative data consist of attributes, labels, or
nonnumerical entries.
Quantitative data consist of numerical measurements
or counts.
TYPES OF DATA (p.g. 9 Larson and
Farber)

Data at the nominal level of measurement are
qualitative only. Data at this level are categorized
using names, labels, or qualities. No mathematical
computations can be made at this level.
Data at the ordinal level of measurement are
qualitative or quantitative. Data at this level can be
arranged in order, or ranked, but differences
between data entries are not meaningful.
LEVELS OF MEASUREMENT(p.g. 10
Larson and Farber)

Data at the interval level of measurement can be ordered, and
meaningful differences between data entries can be calculated.
At the interval level, a zero entry simply represents a position
on a scale; the entry is not an inherent zero.
Data at the ratio level of measurement are similar to data at
the interval level, with the added property that a zero entry is
an inherent zero. A ratio of two data values can be formed so
that one data value can be meaningfully expressed as a
multiple of another.
LEVELS OF MEASUREMENT(p.g. 10
Larson and Farber)

An inherent zero is a zero that implies “none.” For
instance, the amount of money you have in a savings
account could be zero dollars. In this case, the zero
represents no money; it is an inherent zero. On the
other hand, a temperature of does not represent a
condition in which no heat is present.
The temperature is simply a position on the Celsius
scale; it is not an inherent zero

67 90 74 71 90 73 74 70 95 51
69 85 84 72 80 50 89 83 72 91
79 78 75 87 76 91 76 87 82 62
70 86 57 73 82 64 88 81 96 71
91 77 66 83 90 74 85 75 81 80
Frequency
Class
Intervals
3 50-59
5 60-69
18 70-79
16 80-89
8 90-99
50 Total

We will learn how to create:
•Frequency table.
•Relative frequency table.
•Percentage frequency table.
•Cumulative frequency table.
Organization Data

A frequency distribution is a table that shows classes
or intervals of data entries with a count of the number
of entries in each class. The frequency f of a class is a
number of data entries in the class.
Definition of frequency table
(frequency distribution) (p.g. 38
Larson and Farber)

250 150 250 325 70 350 200 400 130 90
130 300 450 160 200 59 130 150 270 275
150 170 180 95 250 200 400 200 100 220
Example 1 p.g. 39 Larson and Farber :
The following sample data set lists the prices (in dollars) of 30
portable global positioning system (GPS) navigators. Construct
a frequency distribution that has seven classes.

For large samples, we can’t use the simple frequency
table to represent the data.
We need to divide the data into groups or intervals or
classes.
So, we need to determine:
•First step :the number of intervals (k).
•Second step :the range (R).
•Third step :the Width of the interval (w).
Frequency distribution for quantitative data

A small number of intervals are not good because
information will be lost.
A large number of intervals are not helpful to
summarize the data.
A commonly followed rule is that 5 k 20
We select 7 intervals in our example.
The number of intervals (k)

It is the difference between the maximum and the
minimum observation (entries) in the data set.
R = the maximum entry - the minimum entry
The range (R)

250 150 250 325 70 350 200 400 130 90
130 300 450 160 200 59 130 150 270 275
150 170 180 95 250 200 400 200 100 220
Example 1 p.g. 39 Larson and Farber :
The following sample data set lists the prices (in dollars) of
30 portable global positioning system (GPS) navigators.
Construct a frequency distribution that has seven classes.

Find the class width as follows. Determine the range of
the data, divide the range by the number of classes, and
round up to the next convenient number.
Class intervals generally should be of the same width.
W=391/7 = 55.86 Round up to 56.
The Width of the interval (w)

Forth step:
Choose the minimum observation to be the lower limit of the
first interval and add the width of interval to get the lower
limit of the second interval and so on
the lower limit of the second interval
59+56=115
the lower limit of the third interval
115+56=171
the lower limit of the fourth interval
171+56=227
the lower limit of the fifth interval
227+56=283
the lower limit of the sixth interval
283+56=339
the lower limit of the seventh interval
339+56=395

Fifth step:
The upper limit of the first class is one less than the lower limit of the second
class.
the upper limit of second interval 171-1=170
the upper limit of third interval 227-1=226
the upper limit of fourth interval 283-1=282
the upper limit of first interval 115-1=114
the upper limit of fifth interval 339-1=338
the upper limit of sixth interval 395-1=394
the upper limit of seventh interval 394+56=450

frequency tally Class interval
59-114
115-170
171-226
227-282
283-338
339-394
395-450
Total

frequency Tally Class interval
5 |||| 59-114
115-170
171-226
227-282
283-338
339-394
395-450
Total

5 |||| 59-114
8 |||| ||| 115-170
171-226
227-282
283-338
339-394
395-450
Total

5 59-114
30 Total

Table(2): Frequency Distribution for
Prices (in dollars) of GPS Navigators
frequency Class interval
30 Total

the class lower boundary= the lower limit – (0.5)
the class upper boundary= the upper limit + (0.5)
Definition of the Class boundaries intervals
Class boundaries are the numbers that separate classes
without forming gaps between them. If data entries are
integers, subtract 0.5 from each lower limit to find the lower
class boundaries. To find the upper class boundaries, add 0.5
to each upper limit. The upper boundary of a class will equal
the lower boundary of the next higher class.

frequency class boundary Class interval
5 58.5-114.5 59-114
8 114.5-170.5 115-170
6 170.5-226.5 171-226
5 226.5-282.5 227-282
2 282.5-338.5 283-338
1 338.5-394.5 339-394
3 394.5-450.5 395-450
30 Total

The midpoint of a class is the sum of the lower
and upper limits of the class divided by two.
The Mid-interval (Midpoints)
=(the lower limit+ the upper limit)/2
Definition of the Mid-interval (Midpoints)

•
frequency midpoint class interval
5 86.5 59-114
8 142.5 115-170
6 198.5 171-226
5 254.5 227-282
2 310.5 283-338
1 366.5 339-394
3 422.5 395-450
30 Total

The relative frequency of a class is the portion
or percentage of the data that falls in that class.
To find the relative frequency of a class, divide
the frequency (f) by the sample size (n).
Definition of the relative frequency

the relative
frequency
frequency Class interval
0.17 5 59-114
0.27 8 115-170
0.2 6 171-226
0.17 5 227-282
0.07 2 283-338
0.03 1 339-394
0.1 3 395-450
1 30 Total
the relative frequency

the percentage frequency = the relative
frequency 100
Definition of the percentage frequency

0.17×100
0.27×100
The percentage
frequency
Frequency Class interval
17 5 59-114
27 8 115-170
20 6 171-226
17 5 227-282
7 2 283-338
3 1 339-394
10 3 395-450
100 30 Total
the percentage frequency table

The cumulative frequency of a class is the sum
of the frequencies of that class and all previous
classes. The cumulative frequency of the last
class is equal to the sample size n.
Definition of The cumulative frequency

Ascending cumulative frequency table
Cumulative
frequency
Frequency Class interval
5 5 59-114
13 8 115-170
19 6 171-226
24 5 227-282
26 2 283-338
27 1 339-394
30 3 395-450
30 Total

Find from the table:
• The Width of the interval
• The midpoints
• class boundaries
• The relative frequency of
intervals.
• The percentage frequency of
intervals.
frequency
Class
interval
100 16-20
122 21-25
900 26-30
207 31-35
795 36-40
568 41-45
322 46-50
Example

Summary of lecture
In these lecture we create:
•frequency table
•the percentage frequency
table
•the relative frequency table
• cumulative frequency table

⮚Ex1.1, P 6: 1,2,3,4,5,6, 8 , 9, 10,11, 12, 13, 14,15,
19;
⮚Ex1.2, P 13: 7, 8, 9, 10,14, 15, 18;
⮚ Ex 2.1, P 47: 11, 12, 14, 31, 32,33.
Homework
From (Larson and Farber)

first lecture to elementary statistcs

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