Unit 1 Exploring Data: Distributions Topic 1 Data and Variables (page 3)

OVERVIEW Statistics is the science of reasoning from data, so a natural place to begin your study is by examining what is meant by the term, “data.” The most fundamental principle in statistics is that of variability. Indeed, if the world were perfectly predictable and showed no variability, there would be no reason to study statistics.

Thus, you will also discover the notion of a variable and consider different classifications of variables. You will also begin to explore the notion of the distribution of a set of data measuring a particular variable. Question: Did you hear the one about the statistician? Answer: Probably

Do the Preliminaries (pages 4 & 5) Clarifications on Questions

#4 Definitions

#6 (1) - Political Views Liberal – open to new behavior or opinions and willing to discard traditional values. Moderate – not radical or excessively right or left wing. Conservative – holding to traditional attitudes and values and cautious about change or innovation.

How can you describe and represent data? Essential Question How can you describe and represent data?

Activity 1-1 Word Lengths (pages 5 & 6) Record the number of letters in each word in the sentence to your answer to question #1 in the Preliminaries.

data data context NO variability vary name 1 here The numbers recorded are called ___________. Not all numbers are . Data are numbers collected in a particular _________. (b) Did every word you wrote contain the same number of letters? Data vary, and _______________ abounds both in everyday life and in academic study. The students in this class _______with respect to gender, length of signature, number of states visited, and lots of other variables like ____________________. data context NO variability vary name 1 here

variable case observational quantitative measurement categorical A __________________ is any characteristic of a person or thing that can be assigned a number or a category. The person or thing to which the number or category is assigned is called the ______ or _____________ unit. A __________________ or _________________ variable is one that measures a numerical characteristic. A __________________ or _________________ variable is one that simply records a category designation. _______________ variables are categorical variables for which only possible categories exist. case observational quantitative measurement categorical qualitative Binary two

How can you describe and represent data? Essential Question How can you describe and represent data?

Activity 1-2 Types of Variables (pages 6 to 8) Quantitative or Categorical? categorical - binary?

categorical … categorical - binary … words categorical Hair color: ___________________ Yes or No Gender: ____________________________ Observational units for letters per word: ______________ Type of variable that “size of word” is: _________________ Type of variable “whether … state” is: ________________________ … The number of students does vary from class to class. categorical - binary … words categorical categorical - binary

differ variability distribution distributions visually numerically The values assumed by a variable _________ from case to case, hence the name. Data display __________________. The pattern of this variability is called the ________________ of the variable. Much of the practice of statistics concerns the ________________ of variables, from displaying them ________________ to summarizing them ________________ to describing them _____________. variability distribution distributions visually numerically verbally

How can you describe and represent data? Essential Question How can you describe and represent data?

Activity 1-3 Penny Thoughts (pages 8 & 9)

(a) # responded:______ # voted to retain :_______ proportion :______ # voted to abolish :______ proportion :______ (c) 1.0 - - Proportion 0.8 - 0.6 - 0.4 - 0.2 - 0.0 - | | | | Retain Abolish

Bar graphs display the distribution of categorical variables. (d) Write a minimum of two (2) complete sentences. 1.0 - - Proportion 0.8 - 0.6 - 0.4 - 0.2 - 0.0 - | | | | Retain Abolish

How can you describe and represent data? Assignment Activity 1-7: Types of Variables (continued) (pages 13 & 14) How can you describe and represent data? Prepare for a quiz on Activity 1-8: Types of Variables (continued) (pages 14 & 15)

How can you describe and represent data? Essential Question How can you describe and represent data?

Activity 1-4 Value of Statistics (pages 9 to 11) When a quantitative or measurement variable can assume a fairly _______ number of possible values, one can tally the data by counting the ______________ of each possible response. small frequency

(a) (b) Is there one value that was chosen more than any other? __________ If yes, what is it? ________________ # that gave a response above 5:________ and the proportion:________ # that gave a response below 5:________ and the proportion :________ (d) rating 1 2 3 4 5 6 7 8 9 tally percent Write a minimum of two (2) complete sentences.

Matching The class is in considerable agreement that it is useful. Class:_____ The class generally feels that statistics is useful but to varying degrees and with a few disagreements. Class:_____ The class displays a wide range of opinions, with slight preference toward feeling that statistics is useful. Class:_____ The class is sharply divided on the issue. Class:_____ The class generally feels that statistics is not useful but displays a range of opinions. Class:_____ C D E A B

Activity 1-8: Types of Variables (continued) Prepare for a quiz on Activity 1-8: Types of Variables (continued) (pages 14 & 15) How can you describe and represent data?

How can you describe and represent data? Assignment Activity 1-11: Super Bowls and Oscar Winners (pages 15 & 16) Assignment Activity 1-14: Student Political Views (page 16) How can you describe and represent data?

How can you describe and represent data? Essential Question How can you describe and represent data?

Activity 1-5 Students’ Travels (pages 11 & 12)

states visited by students (a) Visual Display | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 5 10 15 20 25 30 35 40 states visited by students

dotplot distribution small quantitative a ________________. The visual display that you just constructed is called a ________________. Dotplots are useful for displaying the ____________________ of relatively _____________ data sets of _____________________ variables. dotplot distribution small quantitative

states visited by students [Circle you own value on the display] In relation to my peers with regard to the number of states visited, I seem to fall … Show Visual Display | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 5 10 15 20 25 30 35 40 45 states visited by students

states visited by students Based on this display, the accuracy of my guesses in the “Preliminaries” section was … Show Visual Display | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 5 10 15 20 25 30 35 40 45 states visited by students

states visited by students [comment] Write a minimum of four (4) complete sentences. Show Visual Display | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 5 10 15 20 25 30 35 40 45 states visited by students

How can you describe and represent data? Essential Question How can you describe and represent data?

Activity 1-6 Parents’ Ages (pages 12 & 13)

[Trace over the textbook and label the axis.] father | | | | | | | mother | | | | | | | 15 20 25 30 35 40 45 age when first child was born

age when first child was born [comment] Similar in shape … tails off to the right. The mother’s ages tend to be less than the father’s ages. father | | | | | | | mother | | | | | | | 15 20 25 30 35 40 45 age when first child was born

age when first child was born 20 mothers “middle age”:______ years old fathers “middle age”:______ years old [comment] 25 Females appear to have their first child at a younger age than males. father | | | | | | | mother | | | | | | | 15 20 25 30 35 40 45 age when first child was born

WRAP-UP Since statistics is the science of data , this topic has tried to give you a sense of what data are and a glimpse of what data analysis entails. Data are not mere numbers : Data are collected for some purpose and have meaning in some context . The guessing exercises in these activities have not been simply for your amusement; they have tried to instill in you the inclination to think about data in their context and to anticipate reasonable values for the data to be collected and analyzed.

One should always begin analyzing data by looking at a visual display WRAP-UP You have encountered two very important concepts in this topic that will be central to the entire course: variability and distribution . You have also learned to distinguish between quantitative and categorical variables. These activities have also hinted at a fundamental principle of data analysis: One should always begin analyzing data by looking at a visual display (i.e., a “picture”) of the data. …

WRAP-UP You have discovered two simple techniques for producing such displays: bar graphs for categorical variables and dotplots for quantitative variables. The next topic will continue your study of data and variables by introducing you to the use of the graphing calculator, to the idea of manipulating variables, and to the issue of whether a variable adequately measures what it purports to.

Activity 1-8: Types of Variables (continued) Quiz on Activity 1-8: Types of Variables (continued) (pages 14 & 15) Your topic is due! How can you describe and represent data?