KIN 4310 1st Edition Lecture 4 Outline of Last Lecture I Example II Sample Selection III Sample Selection IV Methods of Sampling V Random Sampling VI Systematic Sampling VII Convenience Sampling VIII Stratified Sampling IX Cluster Sampling X Definitions XI Definitions XII Definitions Methodological Design XIII Definitions XIV Strategies to Avoid Confounding Outline of Current Lecture I Key Concept II Definition III Frequency Distributions IV Frequency Distributions continued V Making a Frequency Table VI Frequency Distribution Ages of Best Actresses VII Reasons for Constructing Frequency Distributions VIII Key Concept IX Definitions X Skewness These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute XI Histogram XII Interpreting Histograms XIII Frequency Polygon XIV Dot Plot XV Stemplot Stem and Leaf XVI Pareto Chart XVII Pie Chart XVIII Scatter Plot XIX Box Plot XX Time Series Graph XXI Other Graphs Current Lecture I Key Concept a When working with large data sets it is often helpful to organize and summarize data by constructing a table called a frequency distribution i Whole point is to help organize data so you can understand data and see things with just a glance II Definition a Frequency Distribution or frequency table i Lists data values either individually or by groups of intervals along with their corresponding frequencies or counts ii It s a table of numbers not a graph or illustration III Frequency Distributions a Express the frequency that each score occurs usually in order from smallest to greatest score b Tells how many examinees obtained each score c Tells the range of scores highest score lowest score d Tells us the mode most frequently occurring score IV Frequency Distributions continued a List data values either individually or by groups of interval along with their corresponding frequencies or counts b The interval is called a class or fin c Helpful for summarizing large data sets d Helpful for improving meaningfulness e Provides a basis for constructing graphs f Break up data into bins like a range of values like 10 19 g How many values occurred in that class V Making a Frequency Table a Step 1 Order the scores b Step 2 Count how many of each score i In the example the scores are bins that represent a number c Step 3 Calculate the cumulative frequency i In the example it tells you the value 7 or less occurs 46 times d Step 4 Calculate the relative frequency raw frequency divided by the total number of data points i In the example 3 50 0 06 ii It represents proportions VI Frequency Distribution Ages of Best Actresses a The data in the example is positively skewed b Here median is the best central tendency method to use VII Reasons for Constructing Frequency Distributions a Large data sets can be summarized b We can gain some insight into the nature of data c We have a basis for constructing important graphs VIII Key Concept a Histogram a type of graph that portrays the nature of a data distribution i An illustration of the frequency distribution ii A bar chart where the height of each represents frequency IX Definitions a Symmetric i Distribution of data is symmetric if the left half of its histogram is roughly a mirror image of its right half ii Lots of histograms are usually bell shaped b Skewed i Distribution of data is skewed if it is not symmetric and if it extends more to one side than the other X Skewness a Symmetric i Mode mean median b Skewed to the Left negatively i Mean median mode ii Long tail points to the lef c Skewed to the Right positively i Mode median mean ii Long tail points to the right XI Histogram a A bar graph in which the horizontal scale represents the classes of data values and the vertical scale represents the frequencies XII Interpreting Histograms a One key characteristic of a normal distribution is that it has a bell shape b It s fairly symmetrical its rare to be perfectly symmetrical XIII Frequency Polygon a Uses line segments connected to points directly above class midpoint values b An illustration of frequency distribution but its not a histogram because it is not a bar chart XIV Dot Plot a A graph in which each data value is plotted as a point or dot along a scale of values b Pre computer days XV Stemplot Stem and Leaf a Represents data by separating each value into two parts the stem such as the leftmost digit and the leaf such as the rightmost digit i Pre computer days ii Also shows histogram if you turn your head b Bumpus s Sparrows i Stem plots can get complicated XVI Pareto Chart a A bar graph for qualitative data with the bars arranged in order according to frequencies b Qualitative data c Not a histogram because the x axis is not a numerical axis d Its always going to look like it is positively skewed but it is not its just in frequency order XVII Pie Chart a A graph depicting qualitative data as slices of a pie b Financial people with an agenda use this to really emphasize something XVIII Scatter Plot a A plot of paired x y data with a horizontal x axis and a vertical y axis b Important with correlational studies c Can only construct if you have paired data so one subject has to have two measurements associated with it XIX Box Plot a Boxes represent quartiles Range shown by whiskers extreme values shown as dots b Rule whisker cant be longer than the box c Each box itself has a midline represents the medial and the top of the box 3 rd quartile and the bottom of the box 1st quartile d The top whiskers represent the maximum value e The dots represent the outliers XX Time Series Graph a A graph of data that have been collected at different points in time b x axis is time and it s a line graph c This shows trends over time Other Graphs a Don t make a graph that doesn t make sense b Graphs are supposed to be quick and informative at a glance XXI