Analyze the following graph!

Cummulative Relative Frequency Plot 4 A Frequency is the number of times a given datum occurs in a data set 4 A Relative Frequency is the fraction of times an answer occurs. 4 A Cummulative Relative Frequency is the accumulation of the relative frequencies.

Example: 4 Twenty students were asked how many hours they worked per day. Their responses, in hours, are listed below: 4 5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6, 5, 4, 4, 3, 5, 2, 5, 3

Relative Frequencies

Chapter 1 & 3 The Role of Statistics & Graphical Methods for Describing Data

Descriptive statistics 4 the methods of organizing & summarizing data Create a graph If the sample of high school GPAs contained 10,000 numbers, how could the data be described or summarized? State the range of GPAs Calculate the average GPA

Inferential statistics 4 involves making generalizations from a sample to a population Based on the sample, if the average GPA for high school graduates was 3.0, what generalization could be made? The average national GPA for this year’s high school graduate is approximately 3.0. Could someone claim that the average GPA for PISD graduates is 3.0? No. Generalizations based on the results of a sample can only be made back to the population from which the sample came from. Be sure to sample from the population of interest!!

Types of variables

Discrete (numerical) 4 listable set of values 4 usually counts of items

Continuous (numerical) 4 data can take on any values in the domain of the variable 4 usually measurements of something

Classifying variables by the number of variables in a data set Suppose that the PE coach records the height of each student in his class. Univariate - data that describes a single characteristic of the population This is an example of a univariate data

Classifying variables by the number of variables in a data set Suppose that the PE coach records the height and weight of each student in his class. Bivariate - data that describes two characteristics of the population This is an example of a bivariate data

Classifying variables by the number of variables in a data set Suppose that the PE coach records the height, weight, number of sit-ups, and number of push-ups for each student in his class. Multivariate - data that describes more than two characteristics (beyond the scope of this course) This is an example of a multivariate data

Identify the following variables: 1. the appraised value of homes in Plano 2. the color of cars in the teacher’s lot 3. the number of calculators owned by students at your school 4. the zip code of an individual 5. the amount of time it takes students to drive to school Discrete numerical Continuous numerical Categorical Is money a measurement or a count?

Types (shapes) of Distributions

Symmetrical 4 refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle 4 bell-shaped is a special type –has a center mound with two sloping tails

Uniform 4 refers to data in which every class has equal or approximately equal frequency

Skewed (left or right) 4 refers to data in which one side (tail) is longer than the other side 4 the direction of skewness is on the side of the longer tail

Bimodal (multi-modal) 4 refers to data in which two (or more) classes have the largest frequency & are separated by at least one other class

How to describe a numerical, univariate graph

What strikes you as the most distinctive difference among the distributions of exam scores in classes A, B, & C ?

Scatter Plots Time Plots Scatter Plots – Start by placing the explanatory variable on the x-axis, and the response variable on the y-axis. Then plot each point, and look for tendencies. Positive linear correlation, Negative quadratic correlation, ect. Time Plots – Place the time on the x-axis, and the amount of the y-axis. Plot each point and then connect them. We utilize these to analyze trends as well.