Analyze the following graph!

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Frequency

Frequency

Cummulative Relative Frequency Plot

A Frequency is the number of times a given datum occurs in a data set

A Relative Frequency is the fraction of times an answer occurs.

A Cummulative Relative Frequency is the accumulation of the relative frequencies.

Example: Twenty students were asked how many

hours they worked per day. Their responses, in hours, are listed below:

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 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 involves making generalizations

from a sample to a populationBased 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)

listable set of valuesusually counts of items

Continuous (numerical)

data can take on any values in the domain of the variable

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 setSuppose 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

Discrete numerical

Continuous numerical

Categorical

Categorical

Is money a measurement or a count?

Types (shapes)of Distributions

Symmetricalrefers to data in which both sides

are (more or less) the same when the graph is folded vertically down the middle

bell-shaped is a special type–has a center mound with two

sloping tails

Uniformrefers to data in which every

class has equal or approximately equal frequency

Skewed (left or right)refers to data in which one

side (tail) is longer than the other side

the direction of skewness is on the side of the longer tail

Bimodal (multi-modal)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.