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ISDS 2000 Chapter 1 and 2 review
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For Exam 1 only LSU Asim Shrestha
Terms in this set (64)
Statistics
The language of data to find the right data , use the proper tools and clearly communicate them.
2 Branches of Statistics
Descriptive and Inferential
Descriptive Statistics
Refers to the summary of important aspects of data set by collecting, organizing and presenting data.
Inferential Statistics
Drawing conclusions about a large set of data, called population - based on smaller set of SAMPLE data.
Population
All members of a specified group.
Population Parameter
Numerical/measure characteristic of population (IE- #%)
Subset
Part of larger group (population) (IE-Quartet of Orchestra)
Sample
A subset of a particular population.
Why the need for Sampling?
Obtaining information on the entire population is expensive.
It is impossible to examine every member of the population.
Types of data
Cross-sectional , Time series
Cross-Sectional data
Refers to data collected by recording a characteristic of many subjects at the same point in time. (ex individuals, households, firms, industries, regions, and countries) The tween example.
Time series data
Refers to data collected by recording a characteristic of a subject over several time periods. (ex daily, weekly, monthly, quarterly, or annual observations) Example: monthly sales of cars at a dealership in 2010, daily price of IBM stock in the first quarter of 2010... etc
Data that is collected about many subjects at the same point in time or without regard to differences in time is known as -?
Cross-sectional data.
Data that are collected by recording a characteristic of a subject over several time periods are referred to as?
Time Series Data
variable
When a characteristic of interest differs in kind of degree among various observations.
Qualitative variable
Ex: Race, gender, profession, type of business, the manufacturer of a car and so on.
Quantitative variable
Assumes meaningful numerical values and can be further categorized as either DISCRETE or CONTINUOUS. Ex: Test scores, age, weight.
Discrete Quantitative Variables
Assumes a countable number of distinct values.
Ex: Number of children in a family, number of points scored in a basketball game.
Continuous Quantitative Variables
Can assume an infinite number of values within some interval.
Ex: Weight, height, investment, return.
Qualitative Variables
Nominal, Ordinal
Quantitative Variables
Interval, Ratio
Nominal scale
Represents the least sophisticated level of measurement.
Simply able to group or categorize them.
The Ordinal Scale
reflects a stronger level of measurement. with it we are able to both categorize and rank the data with respect to some characteristic or trait. The weakness with ordinal-scaled data is that we cannot interpret the difference between the ranked values because the actual numbers used are arbitrary. Ex: Excellent rating = 4 vs excellent rating = 100. Differences between categories are meaningless with ordinal data.
The Interval Scale
Data may be categorized and ranked with respect to some characteristic or trait, differences between interval values are equal and meaningful. Thus the arithmetic operations of addition and subtraction are meaningful. No "absolute 0" or starting point defined, meaningful rations may not be obtained. (IE clock times.)
The Ratio Scale
Represents the strongest level of measurement. They have all the characteristics of interval-scaled data as well as a true zero point as origin. This scale is used to measure many types of data in business analysis. Such as sales, profits, and inventory levels are expressed as ratio-scaled data. Measurements such as weight, time and distance are also measure on a ratio scale, since zero is meaningful.
Descriptive statistics
refers to the summary of a data set in the form of tables, graphs, or the calculation of numerical measures.
Inferential statistics
refers to extracting useful information from a sample to draw conclusions.
Population:
complete collection of items with the characteristic we wish to understand.
Discrete variable
assumes a countable number of distinct values(IE number of children or number of points)
continuous variable
can take on any value within an interval. ( IE weight, time height and investment return)
4 Data measurement Categories
Nominal, Ordinal, Interval, Ratio
The Nominal scale (1)
represents the least sophisticated level of measurement. Like categorizing values into a group.
(Qualitative Variables)
Ex: observations that represent labels or names ; information related to gender or race.
Ordinal Scale
Can be categorized and ranked. Stronger in the sense that we can categorize and order the data. However, differences between the ranked values are meaningless. (Qualitative Variables) EX. good, fair, poor, excellent
EX: Rating a product or teacher, (1 being bad 4 being excellent)
Interval Scale
A stronger measurement scale as compared to nominal. data may be categorized and ranked with respect to some characteristic or trait. Arithmetic is relevant. No absolute "0"
(IE-Temperature Measurement example)
Ratio Scale
represents the strongest level of measurement. Ration-scaled data as well as a true zero point of origin.
Measures: Weight, time, and distance.
Business: Sales, profits, and inventory levels.
Consider the number of people in a household. This variable is best categorized as____/
Discrete variable
A Frequency Distribution for Qualitative data
groups data into categories and records how many observations fall into each category. For each category's frequency, count the days that fall in that category
Relative frequency distribution (proportion)
calculate by dividing each category's frequency by the sample size. Dividing by the total number.
A Frequency Distribution for Quantitative data (number)
groups data into intervals called classes, and records the number of observations that fall into each class.
Guidelines: Classes are mutually exclusive, classes are exhaustive. (pie charts and bar charts)
Approximating class width
(largest value - smallest value)/ number of classes
Cumulative frequency distribution (cumulative)
Specifies how many observations fall below the upper limit of a particular class
A relative frequency distribution (proportion)
identifies the proportion or fraction of values that fall into each class.
Class relative frequency = (class frequency / total number of observations)
A Cumulative relative frequency distribution
Gives the proportion or fraction of values that fall below the upper limit of each class.
A histogram
is a visual representation of a frequency or a relative frequency distribution
- Bar height represents the respective class frequency ( or relative frequency)
- Bar width represents the class width.
Shape of Distribution
Typically symmetric or skewed.
- Symmetric is mirror image on both sides of the center.
- Skewed:
1. positively skewed data form a long, narrow tail to the right.
2. negatively skewed data form a long narrow tail to the left.
A Polygon
is a visual representation of a frequency or a relative frequency distribution.
- Plot the class midpoints on x-axis and associated frequency ( or relative frequency on y-axis)
- Neighboring points are connected with a straight line.
An Ogive
is a visual representation of a cumulative frequency or a cumulative relative frequency distribution.
- Plot the cumulative frequency (or cumulative relative frequency) of each class above the upper limit of the corresponding class.
- The neighboring points are then connected.
A stem-and-leaf diagram
Is often a preliminary step when analyzing a data set. It is useful in that it gives an overall picture of where the data are centered and how the data are dispersed from the center.
provides a visual display of quantitative data
- It gives an overall picture of the data's center and variabilityS
- Each value of the data set is separated into two parts: The Stem consists of the leftmost digits, while the leaf is the last digit.
Characteristics of Stem-and-Leaf
-Most effective for relatively small data sets
-can be used to determine minimum, maximum, range, mode.
- gives an idea of how the individual values are distributed across the range of the data
- retains all data : each observation remains distinctly identifiable.
One method of graphical presentation for qualitative data is a
Pie chart, bar chart
A bar chart
is a useful graphical tool for qualitative data.
One of the primary goals when constructing a frequency distribution for quantitative data is to summarize the data in a manner that
accurately depicts the data as a whole.
When a researcher examines quantitative data and wants to know the number of observations that fall below the upper limit of a particular class, the researcher is best served by creating a
Cumulative frequency distribution.
A relative frequency distribution for quantitative data identifies the
proportion of observations that occur in each class.
What graphical tool is best used to display the relative frequency of grouped, quantitative data?
Histogram.
Which of the following graphical depictions allows you to examine the relationship between two variables?
Scatterplot.
Histograms can be used for all of the following except:
Observe individual data points. (the actual data points are not observed in a histogram)
In descriptive statistics, a polygon is best described as
A graph that plots the midpoints of each class of a frequency distribution.
How does an ogive differ from a polygon?
An Ogive is a graph of cumulative (relative) frequency distribution while a Polygon is a graph of a (relative) frequency distribution.
TO APPROX CLASS WIDTH
(Larges value - smallest value) / total classes = width
A cumulative relative frequency distribution for quantitative data identifies the
PROPORTION of observations that fall below the upper limit of each class.
Which of the following graphical depictions is useful for observing the spread of the data for a single variable?
Histogram.
Stem-and-Leaf diagrams can be used to
-Analyze the shape of the data.
- Determine how dispersed the data is.
- Observe individual data points.
A ____ is a type of graph that allows researchers to examine the relationship between two variables.
Scatterplot
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