Plotting and Smoothing data | Bài giảng số 3 chương 2 học phần Applied statistics | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

APPLIED STATISTICS COURSE CODE: ENEE1006IU Lecture 3:
Chapter 2: Plotting and Smoothing data
(3 credits: 2 is for lecture, 1 is for lab-work)
Instructor: TRAN THANH TU Email: tttu@hcmiu.edu.vn tttu@hcmiu.edu.vn 1 2.1. PLOTTING DATA
•The first step in data analysis should be to plot the data. Graphing data should be
an interactive experimental process.
•Make a variety of graphs to view the data in different ways. Doing this may:
1. Reveal the answer so clearly that little more analysis is needed
2. Point out properties of the data that would invalidate a particular statisticalanalysis
3. Reveal that the sample contains unusual observations
4. Save time in subsequent analyses
5. Suggest an answer that you had not expected6. Keep you from doing something foolish tttu@hcmiu.edu.vn tttu@hcmiu.edu.vn 2 2.1. PLOTTING DATA
Number (frequency) The relative frequency of observations 100 frequency of a class is
in Divided by n of a class equals the the relative frequency
each of several non- fraction or proportion overlapping multiplied by 100.
of observations categories or classes. belonging to a class.
A frequency distribution is a tabular summary of A A percent frequency relative frequency distribution data showing the number distribution gives a summarizes the
(frequency) of tabular summary of data observations in percent frequency of each of
showing the relative several non-overlapping the data for each class.
frequency for each categories or classes. class. 3 The percent Multiply 2.1. PLOTTING DATA
•Displays Used to Show the Distribution of Data:
Bar Chart: show the frequency distribution and relative frequency distribution for categorical data
Pie Chart: show the relative frequency and percent frequency for categorical data
Dot Plot: show the distribution for quantitative data over the entire range of the data
Histogram: show the frequency distribution for quantitative data over a set of class intervals
Stem-and-Leaf display: show both the rank order and shape of the distribution for quantitative data tttu@hcmiu.edu.vn 4 2.1. PLOTTING DATA
•Displays Used to Show the Distribution of Data:
Bar Chart: show the frequency, relative frequency, percent frequency
distributions for categorical data tttu@hcmiu.edu.vn •
On one axis of the chart (usually the horizontal
axis), we specify the labels that are used for the classes (categories). •
A frequency, relative frequency, or percent
frequency scale can be used for the other axis of
the chart (usually the vertical axis). 5 2.1. PLOTTING DATA
•Displays Used to Show the Distribution of Data:
Pie Chart: show the relative frequency and percent frequency distributions for categorical data tttu@hcmiu.edu.vn
• First, draw a circle to represent all the data.
• Then, use the relative frequencies to subdivide the
circle into sectors, or parts, that correspond to the
relative frequency for each class. 6 2.1. PLOTTING DATA
•Displays Used to Show the Distribution of Data:
Dot Plot: show the distribution for quantitative data over the entire range of the data tttu@hcmiu.edu.vn
• A horizontal axis shows the range for the data.
• Each data value is represented by a dot placed above the axis. 7 2.1. PLOTTING DATA
•Displays Used to Show the Distribution of Data:
Histogram: show the frequency distribution for quantitative data over a set of class intervals tttu@hcmiu.edu.vn
• Place the variable of interest on the horizontal axis and the frequency, histogram contains no natural
relative frequency, or percent
separation between the rectangles
frequency on the vertical axis.
• Draw a rectangle whose base is determined by
the class limits on the horizontal axis and whose
height is the corresponding frequency, relative
frequency, or percent frequency. 8 2.1. PLOTTING DATA
•Displays Used to Show the Distribution of Data: tttu@hcmiu.edu.vn
Stem-and-Leaf display: show both the rank order and shape of the distribution for quantitative data
• The stem-and-leaf display is easier to construct by hand.
• Within a class interval, the stemand-leaf
display provides more information than the
histogram because the stem-and-leaf shows the actual data. 9 tttu@hcmiu.edu.vn lOMoARcPSD|47231818 2.1. PLOTTING DATA
•Displays Used to Make Comparisons:
Side-by-Side bar Chart: a graphical display for depicting multiple bar charts on the same display compare two variables tttu@hcmiu.edu.vn 10 lOMoARcPSD|47231818 2.1. PLOTTING DATA
•Displays Used to Make Comparisons:
Stacked bar Charts: a bar chart in which each bar is broken into rectangular
segments of a different color showing the relative frequency of each class in a
manner similar to a pie chart.
compare the relative frequency or percent
frequency of two categorical variables tttu@hcmiu.edu.vn 11 lOMoARcPSD|47231818 2.1. PLOTTING DATA
•Displays Used to Show Relationships:
Scatter plot/diagram: show the relationship between two quantitative variables.
Trendline: approximate the relationship of data in a scatter diagram. tttu@hcmiu.edu.vn 12 lOMoARcPSD|47231818 2.1. PLOTTING DATA •Scatterplot:
•Simple scatterplots are often made before any other data analysis is considered.
•The insights gained may lead to more elegant and informative graphs, or suggest a promising model.
•Linear or nonlinear relations are easily seen, and so are outliers or other aberrations in the data. tttu@hcmiu.edu.vn 13 lOMoARcPSD|47231818 lOMoARcPSD|47231818 tttu@hcmiu.edu.vn 14 2.2. SMOOTHING DATA
•Smoothing is drawing a smooth curve through data in order to eliminate the
roughness (scatter) that blurs the fundamental underlying pattern.
•Smoothing can be thought of as a decomposition of the data.
•In smoothing, the analogous expression is: Data = smooth + rough tttu@hcmiu.edu.vn 15 lOMoARcPSD|47231818 2.2. SMOOTHING DATA
•The simplest smoothing method is to plot the data on a logarithmic scale (or plot
the logarithm of y instead of y itself).
•A logarithmic scale is a nonlinear scale often used when analyzing a large range of quantities.
•Smoothing by plotting the moving averages (MA) or exponentially weighted
moving averages (EWMA) requires only arithmetic (addition, subtraction, multiplication and division).
•The choice of a smoothing method might be influenced by the application. tttu@hcmiu.edu.vn 16 lOMoARcPSD|47231818 2.2. SMOOTHING DATA
•Plotting on a Logarithmic Scale: tttu@hcmiu.edu.vn 17 lOMoARcPSD|47231818 2.2. SMOOTHING DATA
•Smoothing by plotting the moving averages (MA): Moving averages are a simple
and common type of smoothing used in time series analysis and time series forecasting.
Calculating a moving average involves creating a new series where the values
are comprised of the average of raw observations in the original time series. tttu@hcmiu.edu.vn 18