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# INTRODUCTORY STATISTICS CH 2 NOTES MATH 10041-007

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This 4 page Class Notes was uploaded by Marissa Nichol on Thursday September 10, 2015. The Class Notes belongs to MATH 10041-007 at Kent State University taught by Xianglan Bai in Summer 2015. Since its upload, it has received 98 views. For similar materials see INTRODUCTORY STATISTICS in Math at Kent State University.

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Date Created: 09/10/15

INTRODUCTORY STATISTICS CH 2 21 Keep in mind that using graphicsvisuals to see patterns is an important part of data The way that the data is organized Helps examine variation and compare groups of data Two step process 1 See it 2 Summarize it The amount of times the same value is shown in a set of data TYPES OF DISTRIBUTIONS Using dots to mark where each value is above on a number line This makes it easy to see the frequency of the values These looks like bar graphs but the bars are called bins The higher the bin on the number line the more frequent that value is o If a number is chosen that lies on the line between two different bins you can choose either the left or the right side but make sure you always choose the same side when this happens 0 The wider the bin the less detail is shown A proportion that describes how many observations are in one bin ex instead of saying there are 3 observations in a bin you would say there are 312 025 12 being the total amount of observations in the data set TO SEE VISUAL EXAMPLES OF DISTRIBUTIONS SEE PAGES 3740 a visual to use when use when you can t use technology and the set of data isn t large Leaf last digit in observation 0 Stem all the digits before the leaf ex for the 84 8 is the stem amp 4 is the leaf TO SEE A VISUAL OF A STEM AND LEAF PLOT GO TO UPPER RIGHT OF PAGE 41 22 center of the distribution spread in the distribution Things to pay attention to when examining distributions of data 1 3 basic characteristics 0 If the distribution is symmetric or skewed o The of mounds that appear 0 If there are unusually small or large values A symmetric distribution is when the left and right side of the graph are mirror images of each other When the two sides of the graph are not mirror images of each other that is a skewed distribution When there is a there is a quottailquot that extends to either side the lower values that decrease the height of the data on a graph which makes a or a TO SEE A BELL SHAPED DISTRIBUTION GO TO BOTTOM OF PAGE 42 One mound shown in distribution two mounds shown in distribution more than two mounds in distribution TO SEE WHAT A MOUND LOOKS LIKE GO TO PAGE 44 points of value that don t t the pattern of the set of data Sometimes they re mistakes sometimes they re not ex if students record their weight around 100 and a student accidentally writes 1000 1000 would be an outlier 2 The typical value or the value in the middle of the set of data however there is no set center value because it is chosen by your own opinion 3 the variation of values of data If the values are the samesimilar then the dotplot or histogram will be slim If the values are very different then the distribution will be spread out 23 categorica and numerical variables are visualized the same when it comes to data a bar represents each category observed on a number line The height of each bar is relevant to the frequency of the category Differences between bar graphs and histograms The order of bars in a bar chart do not matter When they are sorted from most to least frequent that is called a o The widths of bars in a bar chart have no meaning 0 The bars in a bar chart have gaps between them but in a histogram when there is a gap that means there is no value for that interval Format to display frequencies of data It is a circle or a pie that is sliced into different sections that represent a category for the data set The size of each slice are proportionate to the frequency of value of that category 0 ex if 50 of the data set is the category unknown then the slice would be exactly 12 of the circle 0 not commonly used for statisticians bc it isn t easy to see how big the area of each slice is or to compare variables for different groups just by looking at it 24 The category that occurs most often Categorical variable 1 Called Bimodal if 2 of the categories are the same or almost the same for the most frequent outcomes 2 Called multimodal if more than 2 of the categories are similar in value and are the tallest bars 0 Numerical variable 1 the heights of the tallest mounds don t have to be the same exact height to be multimodal high diversity in different categories high variability c not just about frequency for each category also measured by how many categories have responses 25 false impressions 1 When the pictures are not proportionate to the actual numbers provided 2 When the vertical axis on a graph does not start with O the value seems lower than it is MOST COMMON FOR VISUALS OF MISLEADING GRAPHS SEE PAGE 55 amp 56

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