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# INTRODUCTORY STATISTICS EXAM 1 STUDY GUIDE (CH1/2) MATH 10041-007

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This 9 page Study Guide was uploaded by Marissa Nichol on Sunday September 13, 2015. The Study Guide belongs to MATH 10041-007 at Kent State University taught by Xianglan Bai in Summer 2015. Since its upload, it has received 286 views. For similar materials see INTRODUCTORY STATISTICS in Math at Kent State University.

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Date Created: 09/13/15

STATISTICS EXAM STUDY GUIDE CH12 11 Collecting and analyzing observations to answer question about our surroundings and the universe fundamental concept different versions of a piece of data ex drawing three circles that are three different sizes Numbers in context ex the three circles are recorded by comparing diameterscircumferences REFER TO PAGE 4 FOR MORE EXAMPLES FOR THE INFO ABOVE 12 characteristics of people or things ex gender and weight data grouped into a collection 0 Sample is just one piece of the population a data set that includes information about everyoneeverything observed REFER TO PAGE 6 FOR EXTRA DETAILS ON EACH DEFINITION ABOVE Most important part of data When recording data record extra supporting information ex askanswer the question quothow were the variables measuredquot REFER TO PAGE 67 TO SEE PROPER QUESTIONS TO ASKANSWER 2 TYPES 1 quantities of objects in numbers ex weight of an infant 2 qualities of objects ex gender of an infant FOR PRACTICE ON IDENTIFYING VARIABLES GO TO PAGE 8 Numbers representing a category ex the number 1yes The number Ono Categoryfemae girl1 boy0 the number 1 does belong to the category and the number 0 does not belong Data stored in a spreadsheetlike format A variable is represented in each column variables from different groups are represented in each column SEE PAGE 9 FOR EXAMPLES OF STACKED DATA amp UNSTACKED DATA In class day 1 i symbol for the average of a sample u symbol for the average of the population using chance and selecting people at random as samples of the population n sample N population a list of each person in a population Using random numbers to determine the sample When the population is separated into different groups called strata that do not overlap and a simple random sample is taken from each group The people used at samples must be similar For example girls and boys are separated When you select every quotnthquot from the population and the rst one corresponds to a random number between 1 and n When you select all of the individuals that are in a random group orcoHchon When a sample is contained because it is easier access and rather than doing it by randomness 1 SelfselectedNoluntary samples the person taking the survey participates in it themselves ex using the internet phone or radio to collect answers From the book 13 organizessummarizes two related categorical variables and compares them REFER TO OF PAGE 13 TO SEE EXAMPLE OF HOW THIS WORK how many times a value occurs in a data set 14 One thing or variable being the effect of another variable 1 Treatment variable the tool being used to observe change in behavior of the subjects ex If students are being tested on if paper note taking works better over computer note taking the paper and computer are the treatment variable 2 OutcomeResponse variable records the respond to the treatment variable 3 People who receive the treatment variable are in the treatment group and those who don t are in the controlcomparison group 4 Anecdote Evidence or a story told of someone s experience with something which is used for observations ex Someone tells the story of how eating peanut butter stopped their hair loss FOR EXAMPLES OF ABOVE DEFINITIONS SEE PAGE 14 amp 15 When a subject thinks there is a change because they are given a treatment whether that treatment works or not The psychological effect ex thinking a pain in your body stopped hurting simply just because you took a pill that someone said works When a subject in a study is observed and recorded for their natural actions rather than a researcher controlling where they are placed or what they are doing 1 Compares the outcome variable of the control group to the outcome variable of the treatment group The reason why the outcomes between two different groups are different FOR EXAMPLES OF ABOVE DEFINITIONS SEE PAGE 16 When researchers are in control of the subjects in a treatment group and control group that are alike in every way except for one receiving a treatment while the other one does not 0 Four key features 1 Sample sizearge so there is a variety of the subject being studied 2 The subjects assigned to each group must be at random ex using a computer or ipping a coin 3 Supposed to be quotdoubleblind de nition is below in notes 4 Supposed to use a placebo ex medical treatment both groups must receive same attention FOR EXAMPLES ON HOW THESE WORK SEE PAGES 1819 when the results of a study are persuaded in a certain direction To avoid this the blinding and doubleblind method is used when either researchers or the subject don t know who is assigned to which group until after the study is concluded when both the researchers and subjects don t know which group they re assigned to When reading a study ask yourself 0 which kind of experiment it was controlled or observational 0 how large the sample size was 0 if it follows the four key features shown above 0 if it has been peerreviewed o if it followed the subjects long enough PRACTICE ON HOW TO ANSWER THESE QUESTIONS IS ON PAGE 2123 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 categorical 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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