Describing Data and Distributions PDF

DESCRIBING DATA AND DISTRIBUTIONS Please don’t forget to sign the attendance sheet and grab a set of colored notecards.  INTRODUCTION One of the main purposes in statistics is to make sense out of a large amount of data. There are a few common methods to summarize...

DESCRIBING DATA AND DISTRIBUTIONS Please don’t forget to sign the attendance sheet and grab a set of colored notecards.  INTRODUCTION One of the main purposes in statistics is to make sense out of a large amount of data. There are a few common methods to summarize data Charts Graphs CAT EGOR ICA L VS N UMERI CA L VA RIA BL ES Categorical Numerical Variables Variables Totals or The result of any Nominal and Interval and frequencies from sort of Ordinal variables Ratio variables each category measurment FREQUENCY DIS TRIBUTIONS: TABLES AND GRAPHS "Frequency": A value that describes the number of times or how often a category, score, or range of scores occur. "Frequency Distribution Table": A tabular summary display for a distribution of data organized or summarized in terms of how often a category, score, or range of scores occurs. A frequency distribution summarizes how often a value or range of values is counted in a data set. FRE QUE NC Y Continuous data can be summarized D IS TR IB UTI ON S: graphically using histograms TA BLE S A ND GRA PH S Discreate data is often summarized in a bar chart or a pie chart  HISTOGRAMS “Histograms”: A graphical display used to summarize the frequency of continuous data that are distributed in numeric intervals using bars connected at the upper limits of each interval. H I S TO G R A M S  BAR CHART S “Bar Charts”: A graphical display used to summarize the frequency of discrete and categorical data using bars to represent each frequency.  BAR CHARTS  BAR CHART OF OUR CL ASS  PIE C HART S “Pie Charts”: A graphical display in the shape of a circle that is used to summarize the relative percent of discrete and categorical data into sectors  DISTRIBUTIONS A distribution refers to the number of times every value occurs in a sample or population. Distributions can be either uniform, normal, or skewed  UNIFORM DISTRIBUTIONS “Uniform Distributions”: Every value appears with a similar frequency, proportion, or probability. Examples: Dice, coins, cards  NORMAL DISTRIBUTIONS “Normal Distributions”: A normal distribution curve peaks at the mean values, and then symmetrically tapers off on both sides with 50% of the data points above the mean and 50% of the data points below the mean. If you were to draw a straight line through the middle of the distribution, the two sides would mirror each other.  There are two main types of normal distributions: Unimodal and Bimodal “Unimodal Distribution”: A distribution with one distinct peak. “Bimodal Distribution”: A distribution with two distinct peaks. NORMAL D ISTRIB UTION S  SKEW ED DISTRIBUTIONS “Skewed Distributions”: A skewed distribution occurs when the values are not symmetrical and they concentrate more on one side than the other. Labeling skewness depends on the tail  SKEW ED DISTRIBUTIONS “Positively Skewed”: When the distribution mostly concentrates on the left side of the graph with a long tail to the right side. Example: Income distribution in the U.S. is positively skewed with a long tail to the right side. Most people earn a modest income while the top 1% is making close to one million.  SKEW ED DISTRIBUTIONS “Negatively Skewed”: When the distribution mostly concentrates on the right side of the graph with a long tail to the left side. Example: When students are asked what grades the expect to earn in a course, the majority of students answer in the 80s and/or 90s with very few low scores.  DISTRIBUTIONS Why is a normal distribution the most important type of distribution? We assume the dependent variables are normally distributed in a population. We assume that if we analyzed an entire population, the distribution would closely resemble a normal distribution. Most statistical procedures have an assumption that a variable is normally distributed. W H AT T Y P E O F DISTRIBUTION IS THIS? W H AT T Y P E O F DISTRIBUTION IS THIS?  D E CI D I N G W H AT D E SC R I PT I V E S TAT I S T I C S TO U S E ANY QUESTIONS?