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Chapter 2

CHAPTER 2 NOTES.docx

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Department
Communication, Culture and Technology
Course Code
CCT226H5
Professor
Lee Bailey

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CHAPTER 2 NOTES Recall from ch1 that techniques used to describe a set of data as descriptive statistics. Descriptive statistics organize data to show the general shape of the data and where values tend to concentrate, and to highlight unusual or extreme data values. The first procedure we use to describe a set of data is a frequency table. Relative Class Frequencies • You can convert class frequencies to relative class frequencies to show the fraction of the total number of observations in each category. So, a relative frequency captures the relationship between a class total and the total number of observations. • To convert a frequency distribution to a relative frequency distribution, each of the class frequencies is divided by the total number of observations. For examples, 58/98 (the fraction of apartments listed) is 0.5918. Type Number of Listings Fraction Relative Frequency Percent Apartment 58 58/98 0.5918 59.18 House 26 26/98 0.2653 26.53 Townhouse 14 = 98 14/98 0.1429 = 1.000 14.29 =100 Graphic Presentation of Qualitative Data Bar Charts • A graph in which the classes are reported on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars. • READ ON PAGE 18 Pie Charts • A chart that shows the proportion or percent that each class represents of the total number of frequencies. • Look through bookmarks to learn how to make a pie chart properly. DO SOME OF THE EXERCISES FROM THE TEXTBOOK. Constructing Frequency Distributions: Quantitative Data. LOOK AT PAGE 21-25 (Frequency distribution – a grouping of data into mutually exclusive classes showing the number of observations in each class) • First types of information that you collect is called raw data or ungrouped data. This data is unorganized. Raw data is more easily interpreted when it’s organized into a frequency distribution. List Price (\$) Number of Homes \$0 to under \$1 000 000 88 \$1 000 000 to under \$2 000 000 9 \$2 000 000 to under \$3 000 000 1 98 • STEP 1: Decide on the number of classes in order to organize the raw data, to categorize it. Judgement is needed here. The goal is to u se enough groupings or classes to reveal the shape of the distribution. To have enough classes to give insight to the pattern of the data. A USEFUL RECIPE TO TDETERMINE THE NUMBER OF CLASSES IS THE 2 . This guide suggests you select the smallest number (k) for the number of classes such that 2 is greater than the number of observations (n). o In the real estate example, there were 98 listings. So n=98. If we try k=6, which means we would use 6 classes, 2 =64, which is less than 98. Hence, 6 is not enough classes. If we let k=7, then 2 =128, which is greater than 98. So the suggested number of classes is 7. But you don’t have to use 7 as your set number of classes because sometimes there will be unequal interval of classes. • STEP 2: determine the class interval or width. Generally the class interval or width should be the same for all classes. The classes all together must H−L i≥ cover at least the distance from the lowest value in the raw data up to the highest valuk -> . “I” is the class interval, H is the highest observed value, L is the lowest, and k is the number of
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