A. Constructing and interpreting graphical displays of distribution of univriate data (dotplot, stemplot, histogram, cumulative frequency plot)

1. Center = location Spread = variablility
2. Clusters are isolated groups of data points. Gaps refer to missing areas in a data set. 3. Outliers are extreme values, data points that lie significantly outside other values in a data set. Unusual features are gaps and clusters. 4. Shape = Distribution pattern with data

B. Summarizing distribution of univariate data.
1. Mean = add up data values and divide by number of data values Median = list data vlues in order, locate middle data value
2. Range = Maximum – minimum
Interquartile range (IQR) = Q3 –Q1
Standard deviation is the average distance values fall from the mean of graph. 3. Q1(lower quartile) is the 25th percentile of ordered data or median of lower half of ordered data Median (Q2) is the 50th percentile of ordered data

Q3 (upper quartile) is the 75th percentile of ordered data or median of upper half of ordered data Z scores are standarized standard deviation measurments of how far from the center (mean) a data value falls 4.

5. Add or Subtract- the new location summary statistics (mean, median, min, max, Q1, and Q3) shifts accordingly to the addition (or subtraction) of the constant from the old loaction summary statistics. -The new variation (spread) summary statistics (standard deviation, range, interquartile range) do NOT change from the old variation summary statistics. Measurments of variationare not affected by addition (or subtraction) of a constant. Multiply or Divide- if you multiply or divide a constant number to each value in data set, then -the new location summary statistics (mean, median, min, max, Q1, and Q3) changes by the same multiplication (or division) as calculated on the data set from the old location summary statistics. -The new variation (spread) summary staistics (standard...

...HISTOGRAM
INTRODUCTION
Histogram
* Histograms are graphs of a distribution of data designed to show centring, dispersion (spread), and shape (relative frequency) of the data.
* Histograms can provide a visual display of large amounts of data that are difficult to understand in a tabular, or spreadsheet form.
* Ahistogram shows much the same information as a stem plot, though for a given dataset one or the other of these methods of displaying the data may be preferable. Some points to note:
1. Histograms are preferable for larger datasets as stem plots become unwieldy;
2. With histograms, the original data are usually lost;
3. The choice of bin size or number of bins is not restricted, unlike the stem plot;
4. Histograms take more time than a stem plot to construct by hand; therefore stem plots are preferable for a small dataset.
Ogive
* The relative slopes from point to point will indicate greater or lesser increases.
* The graph of the cumulativefrequencydistribution is better known as cumulativefrequency curve or Ogive.
3 K'S
WHAT WE KNOW | WHAT...

...of the others owned 60 or fewer. The remaining student owned 65. The quartiles for the class were 30, 34 and 42 respectively.
Outliers are defined to be any values outside the limits of 1.5(Q3 – Q1) below the lower quartile or above the upper quartile.
On graph paper draw a box plot to represent these data, indicating clearly any outliers. (7) Jan 2001
2) The random variable X is normally distributed with mean 177.0 and standard deviation 6.4.
(a) Find P(166 < X < 185). (4)
It is suggested that X might be a suitable random variable to model the height, in cm, of adult males.
(b) Give two reasons why this is a sensible suggestion. (2)
(c) Explain briefly why mathematical models can help to improve our understanding of real-world problems. (2) Jan 2001
3) A fair six-sided die is rolled. The random variable Y represents the score on the uppermost, face.
(a) Write down the probability function of Y. (b) State the name of the distribution of Y. (2) (1)
Find the value of
(c) E(6Y + 2), (d) Var(4Y – 2)....

...FREQUENCYDISTRIBUTION
WHAT IT IS Frequencydistributions summarize and compress data by grouping it into classes and recording how many data points fall into each class. That is, they show how many observations on a given variable have a particular attribute. For example, a survey is taken of 50 people's favorite color. The frequencydistribution might indicate 15 people selected green, 12 blue, 6 red, 7 yellow, and 10 purple. Converting these raw numbers into percentages would then provide an even more useful description of the data. The frequencydistribution is the foundation of descriptive statistics. It is a prerequisite for both the various graphs used to displaydata and the basic statistics used to describe a data set -- mean, median, mode, variance, standard deviation, and so forth. Note that frequencydistributions are generally used to describe both nominal and interval data, though they can describe ordinal data.
WHEN TO USE IT A frequencydistribution should be constructed for virtually all data sets. They
are especially useful whenever a broad, easily understood description of data
concentration and spread is needed. Most data...

...the iRiver, and the Magic Star MP3. To summarize the consumer responses with a frequency table, how many classes would the frequency table have?
4. Two thousand frequent Midwestern business travelers are asked which Midwest city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. The results were 100 liked Indianapolis best, 450 liked Saint Louis, 1,300 liked Chicago, and the remainder preferred Milwaukee . Develop a frequency table and a relative frequency table to summarize this information.
5. Wellstone, Inc., produces and markets replacement covers for cell phones in a variety of colors. The company would like to allocate its production plans to five different colors: bright white, metallic black, magnetic lime tangerine orange, and fusion red. The company set up a kiosk in the Mall of America for several hours and ask randomly selected people which cover color was their favorite:
Bright white 130
Metallic black 104
Tangerine orange 455
Fusion red 286
A. What is the table called?
B. Draw a bar chart in the table.
C. Draw a pie chart.
D. If Wellstone, Inc., plan to produce million cell phone covers, how many of each color should it produce?
11. Wachesaw Manufacturing, Inc., produced the following number of units in the last 16 days.
27, 27, 27, 28, 27, 25, 25, 28
26, 28, 26, 28, 31, 30, 26, 26
the information is to be organized into a frequency...

...gathering, analyzing, interpreting, and presenting data
• Measurement taken on a sample
• Type of distribution being used to analyze data
Descriptive statistics:
Using data gathered on a group to describe or reach conclusions about that same group only. Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.
Collect, organize, summarize,display, analyze
Eg: According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2002. The statistic 9 describes the number of problems out of every 100 machines.
Inferential statistics:
Using sample data to reach conclusions about the population from which the sample was taken. Statistical inference is the process of using data obtained from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population).
Predict/forecast, make estimates about population behavior based on sample, , test hypothesis, make decisions
Eg 1: TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers.
Eg 2: The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of...

...Part I
Chapter 2
Data Types, DataDisplay and
Summary Statistics
1
Introduction
• Descriptive Statistics vs. Inferential Statistics
•
Descriptive Statistics - Data summarization
•
Inferential Statistics - Use of sample data to make
inferences about a population
parameter.
•
Population: the collection of objects upon which
measurements could be taken.
•
Sample: a subset of the population.
• Variable is the measurable characteristic of an
entity.
2
Types of Data
• Quantitative or Qualitative?
•
Quantitative: presented as numbers permitting
arithmetic
•
•
•
Interest rate
Temperature
Qualitative (categorical): everything else
•
Country of birth
•
Supplier
3
Types of Data
• Univariate or Multivariate?
•
Univariate: one fact for each object in a dataset (“one
column in a spreadsheet”)
•
Multivariate: two or more facts for each object in a
dataset (“many columns in a spreadsheet”)
4
Types of Data
• Discrete or Continuous?
•
Discrete: counted
•
•
•
Cars sold
Number of children
Continuous: measured (always allow “in-between”
values)
•
•
•
Gallons of oil sold
Temperature
What about age? Money?
5
Types of Data
• Ordinal Data
•
Definition: “Qualitative data that has an ordering”
•...

...ASSIGNMENT
ON
BOX PLOT
COURSE CODE: URP1251
COURSE TITLE: STATISTICS FOR PLANNERS |
SUBMITTED BY
MEHEDI MUDASSER
110412
SUBMISSION DATE: 09/05/2012
DISCUSSION OF BOX PLOT GRAPH WITH APPROPRIATE EXAMPLES
The box plot goes back to John Tukey, which published in 1977 this efficient method todisplay robust statistics. Box plots, the term of graphical presentation of data. So it is one of the main parts of statistics because Statistics is the science of collecting, organizing, presenting, analyzing and interpretingdata to assist in making more effective decisions.
Definition
The box plot is a graphical representation of data that shows a data set’s lowest value,...

...What are the characteristics of a population for which a mean/median/mode would be appropriate? Inappropriate?
The analysis of data begins with descriptive statistics such as the mean, median, mode, range, standard deviation, variance, standard error of the mean, and confidence intervals. These statistics are used to summarize data and provide information about the sample from which the data were drawn and the accuracy with which the sample represents the population of interest. The mean, median, and mode are measurements of the “central tendency” of the data. The range, standard deviation, variance, standard error of the mean, and confidence intervals provide information about the “dispersion” or variability of the data about the measurements of central tendency.
MEASUREMENTS OF CENTRAL TENDENCY The appropriateness of using the mean, median, or mode in data analysis is dependent upon the nature of the data set and its distribution (normal vs non-normal). The mean (denoted by x) is calculated by dividing the sum of the individual data points (where Σ equals “sum of”) by the number of observations (denoted by n). It is the arithmetic average of the observations and is used to describe the center of a data set.
mean=x= One of the most basic purposes of statistics is simply to enable us to make sense of large numbers. For...

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