统计学 第二章

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Data Presentation
Data Presentation Qualitative Data Summary Table Bar Graph Pie Chart Dot Plot Pareto Diagram
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Describing Qualitative Data
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Key Terms
A class is one of the categories into which qualitative data can be classified. The class frequency is the number of observations in the data set falling into a particular class. The class relative frequency is the class frequency divided by the total numbers of observations in the data set. The class percentage is the class relative frequency multiplied by 100.
Row Is Category
Major Count Accounting 130 Economics 20 Management 50 Total 200 © 2011 Pearson Education, Inc
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2.2
Graphical Methods for Describing Quantitative Data
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Data Presentation
Data Presentation Qualitative Data Summary Table Bar Graph Pie Chart Dot Plot Pareto Diagram
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2 144677 3 028 4 1 26
2. Data: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
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Data Presentation
Data Presentation Qualitative Data Summary Table Bar Graph Pie Chart Dot Plot Pareto Diagram
Data Presentation Qualitative Data Summary Table Bar Graph Pie Chart Dot Plot Pareto Diagram
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Quantitative Data Stem-&-Leaf Display Frequency Distribution
Quantitative Data Stem-&-Leaf Display Frequency Distribution
Histogram
Dot Plot
1. Horizontal axis is a scale for the quantitative variable, e.g., percent. 2. The numerical value of each measurement is located on the horizontal scale by a dot.
Histogram
Histogram
Count 5 Frequency Relative Frequency Percent 4 3 2 1 0 0 15.5 25.5 35.5 45.5 55.5 Bars Touch
Class 15.5 – 25.5 25.5 – 35.5 35.5 – 45.5 Freq. 3 5 2
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Two Characteristics
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Quantitative Data Stem-&-Leaf Display Frequency Distribution
Histogram
Summary Table
1. Lists categories & number of elements in category 2. Obtained by tallying responses in category 3. May show frequencies (counts), % or both
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Frequency Distribution Table Example
Raw Data: 24, 26, 24, 21, 27 27 30, 41, 32, 38 Class 15.5 – 25.5
Width
Midpoint Frequency 20.5 30.5 40.5
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Data Presentation
Data Presentation Qualitative Data Summary Table Bar Graph Pie Chart Dot Plot Pareto Diagram
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Quantitative Data Stem-&-Leaf Display Frequency Distribution
Histogram
Stem-and-Leaf Display
1. Divide each observation into stem value and leaf value • Stems are listed in order in a column • Leaf value is placed in corresponding stem row to right of bar
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Class 15.5 – 25.5 25.5 – 35.5 35.5 – 45.5
Prop. .3 .5 .2
Class 15.5 – 25.5 25.5 – 35.5 35.5 – 45.5
% 30.0 50.0 20.0
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Data Presentation
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Summation Notation
For the data x1 = 5, x2 = 3, x3 = 8, x4 = 5, x5 = 4
xi 2 = x12 + x2 2 + x32 + x4 2 + x5 2 ∑
i=1 5
= 5 2 + 32 + 8 2 + 5 2 + 4 2 = 25 + 9 + 64 + 25 + 16 = 139
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Lower Boundary
2.3
Summation Notation
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Summation Notation
Most formulas we use require a summation of numbers.
∑x
i=1
n
i
Sum the measurements on the variable that appears to the right of the summation symbol, beginning with the 1st measurement and ending with the nth measurement.
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Quantitative Data Stem-&-Leaf Display Frequency Distribution
Histogram
Frequency Distribution Table Steps
1. Determine range 2. Select number of classes • Usually between 5 & 15 inclusive 3. Compute class intervals (width) 4. Determine class boundaries (limits) 5. Compute class midpoints 6. Count observations & assign to classes
The central tendency of the set of measurements–that is, the tendency of the data to cluster, or center, about certain numerical values.
Central Tendency (Location)
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2.4
Numerical Measures of Central Tendency
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Thinking Challenge
$400,000 $70,000 $50,000 $30,000 $20,000
Quantitative Data Stem-&-Leaf Display Frequency Distribution
Histogram
Data Presentation
Data Presentation Qualitative Data Summary Table Bar Graph Pie Chart Dot Plot Pareto Diagram
Statistics for Business and Economics
Chapter 2 Methods for Describing Sets of Data
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Contents
1. Describing Qualitative Data 2. Graphical Methods for Describing Quantitative Data 3. Summation Notation 4. Numerical Measures of Central Tendency 5. Numerical Measures of Variability 6. Interpreting the Standard Deviation 7. Numerical Measures of Relative Standing
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Learning Objectives
1. Describe data using graphs 2. Describe data using numerical measures
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2.1
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3 5 2
25.5 – 35.5 35.5 – 45.5
Boundaries
(Lower + Upper Boundaries) / 2
Relative Frequency & % Distribution Tables
Relative Frequency Distribution Percentage Distribution