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# SCO 2550 Week 2/Chapter 2 Notes SCO 2550

U of M

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This 4 page Class Notes was uploaded by Colin Fritz on Sunday September 18, 2016. The Class Notes belongs to SCO 2550 at University of Minnesota taught by Kedong Chen in Fall 2016. Since its upload, it has received 39 views. For similar materials see Business Statistics: Data Sources, Presentation, and Analysis in Business statistics at University of Minnesota.

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Date Created: 09/18/16

SCO 2550 Chapter 2 Notes Colin Fritz Chapter 2 covers how to describe sets of data by means of graph interpretation and also individual data interpretation. Describing Qualitative Data To describe qualitative data it can be broken down in different ways to understand each part of the data. Class – categories into which the qualitative data can be classified An example of this is if you are looking at what type of schools high school students went to after they graduated the classes could perhaps be Public College, Private College, Community College, or no further education. Class frequency – number of observations in the data set that fall into a specific class This would be how many students chose to do one of the particular classes. Class relative frequency – class frequency divided by the total number of observations in the data set If ten of the students decided to go to Community College out of the 100 in the class then the class relative frequency would be 10/100 or 0.1 Class percentage – class relative frequency multiplied by 100 The class percentage for the last example would then be 10%. So that is how you can describe particular data, but you might also want to do it graphically. Typically qualitative data is described using a bar graph or a pie chart. This way the classes are very easy to differentiate from one another. Post Secondary Education 11% 10% 34% 45% Private Public Community No Further Education Interpreting Pie Charts As you can see the chart consists of the choices students made after high school. The pie “slices” are the classes of the particular data set that you are working with. The percentages on the graph are the class percentages. The physical size of each “slice” are proportional to Interpreting Bar Graphs each class relative frequency. Bar graphs are relatively self-explanatory. Each bar represents a class and the height of the bar is equivalent to the class relative frequency. Each bar is in order from greatest to least. Describing Quantitative Data Typically quantitative data is described or summarized using dot plots, stem- and-leaf displays, and histograms. Dot plots Dot plots have the numerical value of each data set in a horizontal fashion. When data is repeated a dot is placed on the corresponding number. This type of graph makes finding the frequency very easy. Stem and Leaf Displays A stem and leaf plot is a compact way to represent decimals. The stem is the number to the left of the decimal and the leaf is the number to the right of the decimal place. Numbers on the leaf side are always in order as well. Histograms Histograms are divided into class intervals like bar graphs, but histograms show the distribution of variables. While bar graphs compare them. Other Things to Know Central Tendency – tendency of the data to cluster or center about specific numerical values Variability - the spread of the data Skewed – one tail of the distribution has more extreme observations than the other Types: Median < Mean = skewed right Mean < Median = skewed left Median = Mean = symmetric data Mean – sum of values/number of values Median – middle-most observation Mode – most frequent observation 2 Σ 2 Variance – (sample) – s = ¿ (xi– x-bar) )/n-1 Standard deviation = √ Variance Box plots are also important. They are useful for detecting outliers. - Here is an example of one labeling each important part. The second way to detect outliers is with the z-score method. Z-Score – how far form the mean in terms of std. deviations Z= (xi – mean)/(standard deviation) General Outlier Rule for Z-score Z ≥ 2 - possible outlier Z ≥ 3 - probable outlier

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