Statistics final seminar

Goals
 Understand why we study statistics.
 Explain what is meant by descriptive statistics and inferential
statistics.
 Distinguish between a qualitative variable and a quantitative
variable.
 Describe how a discrete variable is different from a continuous
variable.
 Scales of measurement.
2

What is Meant by Statistics?
Statistics is the science of collecting, organizing,
presenting, analyzing, and interpreting numerical data to assist in
making more effective decisions.
A statistic (singular) or sample statistic is a single measure
of some attribute of a sample (e.g., its arithmetic mean value). It is
calculated by applying a function (statistical algorithm) to the
values of the items of the sample, which are known together as
a set of data.
More formally, statistical theory defines a statistic as a
function of a sample where the function itself is independent of the
sample's distribution; that is, the function can be stated before
realization of the data. The term statistic is used both for the
function and for the value of the function on a given sample.
3

Who Uses Statistics?
Statistical techniques are used extensively in :
Marketing
Accounting
Quality control
Consumers
Professional sports people
Hospital administrators
Educators
Politicians
Physicians
4

Types of Statistics – Descriptive Statistics
 Descriptive Statistics: Methods of organizing, summarizing, and
presenting data in an informative way.
Example 1: A Gallup poll found that 49% of the people in a
survey knew the name of the first book of the Bible. The statistic
49 describes the number out of every 100 persons who knew the
answer.
Example 2: According to Consumer Reports, General Electric
washing machine owners reported 9 problems per 100 machines
during 2001. The statistic 9 describes the number of problems out
of every 100 machines.
 Inferential Statistics: A decision, estimate, prediction, or
generalization about a population, based on a sample.
5

Population versus Sample
A population is a collection of all possible individuals, objects,
or measurements of interest.
A sample is a portion, or part, of the population of interest
6

Types of Variables
A. Qualitative or Attribute variable - The characteristic being
studied is nonnumeric.
Examples: Gender, religious affiliation, type of automobile
owned, state of birth, eye color are examples.
B. Quantitative variable - Information is reported numerically.
Examples: Balance in your checking account, minutes
remaining in class, or number of children in a family.
7

Quantitative Variables - Classifications
Quantitative variables can be classified as either discrete or
continuous.
A. Discrete variables: can only assume certain values and there are
usually “gaps” between values.
Examples: the number of bedrooms in a house, or the number
of hammers sold at the local Home Depot (1,2,3,…,etc).
B. Continuous variable can assume any value within a specified
range.
Examples: The pressure in a tire, the weight of a pork chop, or the
height of students in a class.
8

Summary of Types of Variables
9

1. Nominal level - data that is
classified into categories and
cannot be arranged in any
particular order.
Examples: eye color, gender,
religious affiliation.
2. Ordinal level – involves data
arranged in some order, but the
differences between data
values cannot be determined or
are meaningless.
Example: During a taste test of 4
soft drinks, Mellow Yellow
was ranked number 1, Sprite
number 2, Seven-up number 3,
and Orange Crush number 4.
3. Interval level - similar to the
ordinal level, with the additional
property that meaningful
amounts of differences between
data values can be determined.
There is no natural zero point.
Example: Temperature on the
Fahrenheit scale.
4. Ratio level - the interval level
with an inherent zero starting
point. Differences and ratios are
meaningful for this level of
measurement.
Examples: Monthly income of
surgeons, or distance traveled by
manufacturer’s representatives
per month.
Four levels of Measurement
10

Characteristics for levels of measurement
11

Describing Data:
Frequency Tables, Frequency
Distributions, and Graphic
Presentation
12

Organize qualitative data into a frequency table.
Present a frequency table as a bar chart or a pie chart.
Organize quantitative data into a frequency distribution.
Present a frequency distribution for quantitative data using
histograms, frequency polygons, and cumulative frequency
polygons.
Goals
13

A Frequency distribution
is a grouping of data into
mutually exclusive categories
showing the number of
observations in each class.
Frequency Distribution
17

 Class frequencies can be converted to relative class frequencies
to show the fraction of the total number of observations in each
class.
 A relative frequency captures the relationship between a class
total and the total number of observations.
Relative Class Frequencies
20

 Class midpoint: A point that divides a class into two
equal parts. This is the average of the upper and lower
class limits.
 Class frequency: The number of observations in each
class.
 Class interval: The class interval is obtained by
subtracting the lower limit of a class from the lower
limit of the next class.
Frequency Distribution
21

Ms. Kathryn Ball of AutoUSA
wants to develop tables, charts,
and graphs to show the typical
selling price on various dealer
lots. The table on the right
reports only the price of the 80
vehicles sold last month at
Whitner Autoplex.
Example- Creating a Frequency Distribution
Table
22

 Step 1: Decide on the number of classes.
A useful recipe to determine the number of classes (k) is the “2 to
the k rule.” such that 2k
> n.
There were 80 vehicles sold. So n = 80. If we try k = 6, which
means we would use 6 classes, then 26
= 64, somewhat less than
80. Hence, 6 is not enough classes. If we let k = 7, then 27
= 128,
which is greater than 80. So the recommended number of classes
is 7.
 Step 2: Determine the class interval or width.
The formula is: i ≥ (H-L)/k where i is the class interval, H is the
highest observed value, L is the lowest observed value, and k is
the number of classes.
($35,925 - $15,546)/7 = $2,911
Round up to some convenient number, such as a multiple of 10
or 100. Use a class width of $3,000
Constructing Frequency Table - Example
23

 Step 3: Set the individual class limits
24

 Step 4: Tally the
vehicle selling prices
into the classes.
 Step 5: Count the
number of items in
each class.
25

To convert a frequency distribution to a relative frequency
distribution, each of the class frequencies is divided by the total
number of observations.
Relative Frequency Distribution
26

The three commonly used graphic forms are:
Histograms
Frequency polygons
Cumulative frequency distributions
Graphic representation of Frequency
Distribution
27

Histogram for a frequency distribution based on
quantitative data is very similar to the bar chart showing the
distribution of qualitative data. The classes are marked on the
horizontal axis and the class frequencies on the vertical axis. The
class frequencies are represented by the heights of the bars.
Histogram
28

 A frequency polygon also
shows the shape of a
distribution and is similar
to a histogram.
 It consists of line segments
connecting the points
formed by the intersections
of the class midpoints and
the class frequencies.
Frequency Polygon
30

Cumulative Frequency Distribution
31

Cumulative Frequency Distribution
32

Statistics final seminar

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Statistics final seminar