Bài giảng nguyên lý thông kê chương 2 summarizing data student

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Chapter Summarizing data Part A Summarizing Qualitative Data Summarizing Quantitative Data Why summarizing data? Survey, investigation Raw data Disadvantage? How to extract some information from these data? - arranging - putting them into order I Summarizing Qualitative Data Frequency Distribution  Relative Frequency Distribution  Percent Frequency Distribution  Bar Graph  Pie Chart  Frequency Distribution AA frequency frequency distribution distribution is is The The objective objective is is Example: Marada Inn Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor The ratings provided by a sample of 20 guests are: Example: Marada Inn Below Average Above Average Above Average Average Above Average Average Above Average Average Above Average Below Average Poor Excellent Above Average Average Above Average Above Average Below Average Poor Above Average Average Why Use Frequency Distributions?    A frequency distribution is a way to summarize data The distribution condenses the raw data into a more useful form and allows for a quick visual interpretation of the data Relative Frequency Distribution The The relative relative frequency frequency of of aa class class is is AA relative relative frequency frequency distribution distribution is is Relative Frequency Distribution Ratings Frequency Poor Below Average Average Above Average Excellent Total 20 Relative frequency Bar Graph  A graphical device for depicting qualitative data  On one axis (usually the horizontal axis), we specify the label or the name of each of the class  On the other axis (usually the vertical axis), we specify the frequency, relative frequency of each class  A bar of fixed width is drawn above each class label, we extend the height appropriately  The bars are separated to emphasize the fact that each class is a separate category Crosstabulation  A crosstabulation is Crosstabulation can be used when: Cross-tabulation Example: Finger Lakes Homes The number of Finger Lakes homes sold for each style and price for the past two years is shown below Crosstabulation  Insights Gained from Preceding Crosstabulation Crosstabulation Frequency distribution for the price variable Price Range < $99,000 > $99,000 Total Colonial Home Style Log Split A-Frame Total 18 12 14 19 16 12 20 35 15 30 Frequency distribution for the home style variable 55 45 100 Cross-tabulation: Row or Column Percentages  Converting the entries in the table into row percentages or column percentages can provide additional insight about the relationship between the two variables Crosstabulation: Row Percentages Crosstabulation: Column Percentages Scatter Diagram and Trendline  A scatter diagram is a graphical presentation of the relationship between two quantitative variables  One variable is shown on the horizontal axis and the other variable is shown on the vertical axis  The general pattern of the plotted points suggests the overall relationship between the variables  A trendline is an approximation of the relationship Scatter Diagram  A Positive Relationship y x Scatter Diagram  A Negative Relationship y x Scatter Diagram  No Apparent Relationship y x Example: Panthers Football Team  Scatter Diagram The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored x = Number of Interceptions 3 y = Number of Points Scored 14 24 18 17 30 Scatter Diagram Example: Panthers Football Team Insights Gained from the Preceding Scatter Diagram Tabular and Graphical Procedures Data Data Qualitative Qualitative Data Data Quantitative Data Data Tabular Tabular Methods Graphical Graphical Methods Methods Tabular Methods Methods •Frequency Distribution •Rel Freq Dist •Crosstabulation •Bar Graph •Pie Chart •Frequency Distribution •Rel Freq Dist •Cum Freq Dist •Cum Rel Freq Distribution •Stem-and-Leaf Display •Crosstabulation Graphical Methods •Dot Plot •Histogram •Ogive •Scatter Diagram [...]... data values, each showing the number of items having that value (the frequency) Data values Frequency 0 10 1 12 2 9 3 8 1 Simple frequency distribution • Normally applicable to discrete raw data Why? Why? • Normally not suitable for continuous data Example  The following data record the number of children in the families of the 47 workers in a company: 1 1 3 2 0 2 0 1 2 2 1 3 5 2 4 0 0 2 4 1 1 2 2... 2 2 0 3 0 0 2 1 3 6 0 2 1 0 3 2 2 2 1 0 0 1 1 3 1 4 Constructing a simple frequency distribution using a tally chart Data value 0 1 2 3 4 5 6 Tally marks Total Frequency distribution table Number of children in family 0 1 2 3 4 5 6 Number of workers Disadvantage of simple frequency distribution 2 Grouped frequency distributions     Used when the data set contains a large number of data values A... Repair Sample of Parts Cost for 50 Tune-ups 91 71 104 85 62 78 69 74 97 82 93 57 72 89 62 68 88 68 98 101 75 52 99 66 75 79 97 105 77 83 68 71 79 105 79 80 75 65 69 69 97 62 72 76 80 109 67 74 62 73 Frequency Distribution  Guidelines for Selecting Width of Classes •Use classes of equal width •Approximate Class Width = Largest Data Value − Smallest Data Value Number of Classes  Example Relative Frequency... summaries data into groups of values, each showing the number of items having values in the group Each group of data value called class Used for both continuous data and discrete data Definitions associated with frequency distribution classes  Class limits: are the lower and upper values of the classes as physically described in the distribution Discrete data Lower limit Classes Continuous data Upper... lower/upper limit - Usually used for the first class which has no defined lower limit and/or the last class which has no defined upper limit Classes < 10 10-15 15 -20 > =20 Guidelines for grouping values into classes •  Use between 5 and 20 classes Number of Data Points Number of Classes Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used... Percent Frequency Distribution Dot Plot One of the simplest graphical summaries of data is a dot plot  A horizontal axis shows the range of data values  Then each data value is represented by a dot placed above the axis  Dot Plot Tune-up Parts Cost Histogram  Another common graphical presentation of quantitative data is a histogram  The variable of interest is placed on the horizontal axis  A... device  Presenting relative frequency distributions for qualitative data First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class  Pie Chart - Example Example: Marada Inn Insights Gained from the Preceding Pie Chart II Summarizing Quantitative Data       Frequency Distribution Relative Frequency Dot Plot... Continuous data Upper limit Lower limit Classes Upper limit Definitions associated with frequency distribution classes Class widths (class lengths): - continuous data: are the numerical differences between lower and upper class limits - discrete data: are the numerical differences between the lower limit of one class and the lower limit of the immediately following class  Class mid-points: are situated
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