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Statistics with Economics and Business Applications
Statistics with Economics and Business Applications
Stem and Leaf Plots
Stem and Leaf Plots
Interpreting Graphs: Shapes
Interpreting Graphs: Shapes
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Statistics with Economics and Business Applications

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1Statistics with Economics and Business 17right. For each measurement, record the
Applications. Chapter 2 Describing Sets of leaf portion in the same row as its
Data Descriptive Statistics - Tables and matching stem. Order the leaves from
Graphs. lowest to highest in each stem.
2Review. I. What’s in last lecture? 1. 18Example. The prices ($) of 18 brands
inference process 2. population and of walking shoes: 90 70 70 70 75 70 65 68
samples II. What's in this lecture? 60 74 70 95 75 70 68 65 40 65.
Descriptive Statistics – tables and 19Interpreting Graphs: Location and
graphs. Read Chapter 2. Spread. Where is the data centered on the
3Descriptive and Inferential horizontal axis, and how does it spread
Statistics. Statistics can be broken into out from the center?
two basic types: Descriptive Statistics 20Interpreting Graphs: Shapes.
(Chapter 2): Methods for organizing, 21Interpreting Graphs: Outliers. Are
displaying and describing data by using there any strange or unusual measurements
tables, graphs and summary statistics. that stand out in the data set?
Descriptive statistics describe patterns 22Example. A quality control process
and general trends in a data set. It measures the diameter of a gear being made
allows us to get a ``feel'' for the data by a machine (cm). The technician records
and access the quality of the data. 15 diameters, but inadvertently makes a
Inferential Statistics (Chapters 7-13): typing mistake on the second entry. 1.991
Methods that making decisions or 1.891 1.991 1.988 1.993 1.989 1.990 1.988
predictions about a population based on 1.988 1.993 1.991 1.989 1.989 1.993 1.990
sampled data. 1.994.
4Variables and Data. A variable is a 23Relative Frequency Histograms. A
characteristic that changes or varies over relative frequency histogram for a
time and/or for different individuals or quantitative data set is a bar graph in
objects under consideration. Examples: which the height of the bar shows “how
Hair color, white blood cell count, time often” (measured as a proportion or
to failure of a computer component. relative frequency) measurements fall in a
5Definitions. An experimental unit is particular class or subinterval.
the individual or object on which a 24How to Draw Relative Frequency
variable is measured. A measurement Histograms. Divide the range of the data
results when a variable is actually into 5-12 subintervals of equal length.
measured on an experimental unit. A set of Calculate the approximate width of the
measurements, called data, can be either a subinterval as Range/number of
sample or a population. subintervals. Round the approximate width
6Example. Variable Hair color up to a convenient value. Use the method
Experimental unit Person Typical of left inclusion, including the left
Measurements Brown, black, blonde, etc. endpoint, but not the right in your tally.
7Example. Variable Time until a light (Different from the guideline in the
bulb burns out Experimental unit Light book). Create a statistical table
bulb Typical Measurements 1500 hours, including the subintervals, their
1535.5 hours, etc. frequencies and relative frequencies.
8How many variables have you measured? 25How to Draw Relative Frequency
Univariate data: One variable is measured Histograms. Draw the relative frequency
on a single experimental unit. Bivariate histogram, plotting the subintervals on
data: Two variables are measured on a the horizontal axis and the relative
single experimental unit. Multivariate frequencies on the vertical axis. The
data: More than two variables are measured height of the bar represents The
on a single experimental unit. proportion of measurements falling in that
9Types of Variables. class or subinterval. The probability that
10Types of Variables. Qualitative a single measurement, drawn at random from
variables measure a quality or the set, will belong to that class or
characteristic on each experimental unit. subinterval.
Examples: Hair color (black, brown, 26Example. The ages of 50 tenured
blonde…) Make of car (Dodge, Honda, Ford…) faculty at a state university. 34 48 70 63
Gender (male, female) State of birth 52 52 35 50 37 43 53 43 52 44 42 31 36 48
(California, Arizona,….). 43 26 58 62 49 34 48 53 39 45 34 59 34 66
11Types of Variables. Quantitative 40 59 36 41 35 36 62 34 38 28 43 50 30 43
variables measure a numerical quantity on 32 44 58 53. We choose to use 6 intervals.
each experimental unit. Discrete if it can Minimum class width = (70 – 26)/6 = 7.33
assume only a finite or countable number Convenient class width = 8 Use 6 classes
of values. Continuous if it can assume the of length 8, starting at 25.
infinitely many values corresponding to 27Age. Tally. Frequency. Relative
the points on a line interval. Frequency. Percent. 25 to < 33. 1111.
12Examples. For each orange tree in a 5. 5/50 = .10. 10%. 33 to < 41. 1111
grove, the number of oranges is measured. 1111 1111. 14. 14/50 = .28. 28%. 41 to
Quantitative discrete For a particular < 49. 1111 1111 111. 13. 13/50 = .26.
day, the number of cars entering a college 26%. 49 to < 57. 1111 1111. 9. 9/50 =
campus is measured. Quantitative discrete .18. 18%. 57 to < 65. 1111 11. 7. 7/50
Time until a light bulb burns out = .14. 14%. 65 to < 73. 11. 2. 2/50 =
Quantitative continuous. .04. 4%.
13Graphing Qualitative Variables. Use a 28Describing the Distribution. Shape?
data distribution to describe: What values Outliers? What proportion of the tenured
of the variable have been measured How faculty are younger than 41? What is the
often each value has occurred “How often” probability that a randomly selected
can be measured 3 ways: Frequency Relative faculty member is 49 or older? Skewed
frequency = Frequency/n Percent = 100 x right No. (14 + 5)/50 = 19/50 = .38 (9+ 7
Relative frequency. + 2)/50 = 18/50 = .36.
14Example. A bag of M&M®s contains 29Key Concepts. I. How Data Are
25 candies: Raw Data: Statistical Table: Generated 1. Experimental units,
Color. Tally. Frequency. Relative variables, measurements 2. Samples and
Frequency. Percent. Red. 5. 5/25 = .20. populations 3. Univariate, bivariate, and
20%. Blue. 3. 3/25 = .12. 12%. Green. 2. multivariate data II. Types of Variables
2/25 = .08. 8%. Orange. 3. 3/25 = .12. 1. Qualitative or categorical 2.
12%. Brown. 8. 8/25 = .32. 32%. Yellow. 4. Quantitative a. Discrete b. Continuous
4/25 = .16. 16%. III. Graphs for Univariate Data
15Graphs. Bar Chart. Pie Chart. Distributions 1. Qualitative or
16Scatterplots. The simplest graph for categorical data a. Pie charts b. Bar
quantitative data Plots the measurements charts.
as points on a horizontal axis, stacking 30Key Concepts. 2. Quantitative data a.
the points that duplicate existing points. Scatterplot b. Stem and leaf plots c.
Example: The set 4, 5, 5, 7, 6. Relative frequency histograms 3.
17Stem and Leaf Plots. A simple graph Describing data distributions a.
for quantitative data Uses the actual Shapes—symmetric, skewed left, skewed
numerical values of each data point. right, unimodal, bimodal b. Proportion of
Divide each measurement into two parts: measurements in certain intervals c.
the stem and the leaf. List the stems in a Outliers.
column, with a vertical line to their
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