UNIT #1CHAPTERS

BY JEREMY GREEN, ADAM PAQUETTEY, AND MATT

STAUB

CHAPTER 2: DATA• THE FIVE W’S

• WHO- THE ROWS OF A DATA TABLE THAT CORRESPOND TO THE INDIVIDUAL CASES ABOUT WHOM WE RECORD SOME STATISTICS.

• WHAT- THE CHARACTERISTICS RECORDED ABOUT EACH INDIVIDUAL

• WHY- REASON DATA WAS COLLECTED

• WHERE- WHERE THE DATA WAS COLLECTED

• WHEN- THE TIME THAT THE DATA WAS COLLECTED

• HOW- IT IS IMPORTANT TO EXPLAIN THE TYPE OF EXPERIMENT, SURVEY, OR STUDY THAT WAS CONDUCTED

• COLLECTED DATA IS ORGANIZED INTO DATA TABLESX Y Z

A 123 34567 56789

B 123345 789 0987654

CHAPTER 2 CONT.• VARIABLES

• MEASURED IN UNITS

• CATEGORICAL VARIABLE- ANSWERS QUESTIONS ABOUT HOW CASES FALL INTO CATEGORIES

• QUANTITATIVE VARIABLE- ANSWERS QUESTIONS ABOUT THE QUANTITY OF WHAT IS MEASURED

• TYPES OF RESPONDENTS

• SUBJECTS- PEOPLE WE EXPERIMENT ON

• EXPERIMENTAL UNITS- ANIMALS, PLANTS, WEB SITES AND OTHER INANIMATE SUBJECTS

• RESPONDENTS- INDIVIDUALS WHO ANSWER A SURVEY

CHAPTER 3: DISPLAYING AND DESCRIBING DATA

• THREE RULES OF DATA ANALYSIS

1. MAKE A PICTURE

2. MAKE A PICTURE

3. MAKE A PICTURE

• FREQUENCY TABLE

• TABLE THAT ORGANIZES COUNTS FOR CATEGORICAL DATA

• RELATIVE FREQUENCY TABLES SHOW PERCENTS

• IMPORTANT TO KNOW PROPORTIONS SO WE CAN USE PERCENTS

• AREA PRINCIPLE- THE AREA OCCUPIED BY A PART OF THE GRAPH SHOULD CORRESPOND TO THE MAGNITUDE OF THE VALUE IT REPRESENTS.

CHAPTER 3 CONT.• BAR CHART- DISPLAYS THE DISTRIBUTION OF A CATEGORICAL VARIABLE, SHOWING THE COUNTS

FOR EACH CATEGORY NEXT TO EACH OTHER FOR EASY COMPARISON.

• PIE CHARTS- SHOWS ALL THE CASES ON AS A CIRCLE AND THEY SLICE THE CIRCLE INTO PIECES WHO SIZES ARE PROPORTIONAL TO THE FRACTION OF THE WHOLE OF EACH CATEGORY.

• CONTINGENCY TABLE

• SHOWS TWO VARIABLES SIDE BY SIDE

• MARGINAL DISTRIBUTION- SHOWS THE COUNTS FOR EACH VARIABLE

• CONDITIONAL DISTRIBUTION- SHOWS THE PERCENTS FOR EACH VARIABLE

• INDEPENDENCE- WHEN THE DISTRIBUTION OF ONE VARIABLE IS THE SAME FOR ALL CATEGORIES OF ANOTHER

AP Stats Grades

A B

C D

F

X Y

A 5678 234567

B 98765 345678

Total 99999 98765

Bar Chart Pie Chart

Contingency Table

CHAPTER 4: DISPLAYING AND SUMMARIZING DATA

• HISTOGRAM- REPRESENTS COUNTS AS BARS AND PLOTS THEM AGAINST QUANTITATIVE DATA.

• RELATIVE FREQUENCY HISTOGRAM- SAME AS HISTOGRAM, REPLACING THE COUNTS ON THE VERTICAL AXIS WITH PERCENTAGES OF THE TOTAL NUMBER OF CASES.

• STEM-AND-LEAF PLOT- SIMILAR TO A HISTOGRAM, BUT IT SHOWS EACH INDIVIDUAL VALUE.

• DOTPLOT- A DOT IS PLACED ALONG AN AXIS FOR EACH CASE IN THE DATA.

• QUANTITATIVE DATA CONDITION- THE DATA ARE VALUES OF A QUANTITATIVE VARIABLE WHOSE UNITS ARE KNOWN. MUST KNOW THIS BEFORE MAKING A GRAPHICAL DISPLAY.

CHAPTER 4 CONT.• THREE THINGS TO DESCRIBE A DISTRIBUTION

1. SHAPE- WHETHER IT UNIMODAL OR BIMODAL, SYMMETRIC OR SKEWED, AND WHETHER OR NOT THERE ARE OUTLIERS.

2. CENTER- THE CENTER OF THE DATA. USUALLY TALKS ABOUT THE MEDIAN.

MEDIAN-IS THE MIDDLE VALUE THAT DIVIDES THE TWO HALVES OF THE HISTOGRAM.

3. SPREAD- THE RANGE AND INTERQUARTILE RANGE OF THE DATA.

RANGE- THE DIFFERENCE BETWEEN THE MAXIMUM AND THE MINIMUM OF THE DATA.

INTERQUARTILE RANGE- THE DIFFERENCE BETWEEN THE UPPER QUARTILE RANGE AND THE LOWER QUARTILE RANGE

• 5 NUMBER SUMMARY- REPORTS THE MEDIAN, QUARTILES, MINIMUM, AND THE MAXIMUM OF A DATA SET.

CHAPTER 4 CONT.• MEAN

• FEELS LIKE THE CENTER BECAUSE IT IS THE POINT WHERE THE HISTOGRAM BALANCES.

• CALCULATED BY DIVIDING THE TOTAL OF YOUR DATA BY THE NUMBER OF DATA POINTS.

• USED WHEN THE HISTOGRAM IS SYMMETRIC AND THERE ARE NO OUTLIERS.

• MEDIAN

• IS RESISTANT TO VALUES THAT ARE EXTRAORDINARILY LARGE OR SMALL

• USED WHEN THE DATA IS SKEWED OR HAS OUTLIERS.

• STANDARD DEVIATION

• ACCOUNTS FOR HOW FAR EACH VALUE IS FROM THE MEAN.

• ONLY WORKS FOR SYMMETRIC DATA.

• CANNOT BE CALCULATED BY ITS SELF, SO YOU MUST TAKE THE SQUARE ROOT OF THE VARIANCE IN ORDER TO OBTAIN THE STANDARD DEVIATION.

CHAPTER 5: UNDERSTANDING AND COMPARING DISTRIBUTIONS

• BOXPLOT- A GRAPHICAL REPRESENTATION OF A 5 NUMBER SUMMARY. ALSO, SHOWS OUTLIERS OF THE DATA.

• OUTLIERS

• ANY POINT THAT HAS LEVERAGE ON THE DATA DUE TO BEING EXTREMELY HIGH OR EXTREMELY LOW.

• TO DETERMINE WHETHER OR NOT A POINT IS AN OUTLIER YOU USE THE FORMULA: 1.5 X IQR THEN SUBTRACT FROM LOWER QUARTILE AND ADD TO UPPER QUARTILE.

• RE-EXPRESSING OR TRANSFORMING DATA- APPLY A SIMPLE FUNCTION TO FIX SKEWED DATA. EX: TAKING THE NATURAL LOG OF YOUR DATA.

• BOXPLOTS ALLOW YOU TO COMPARE MULTIPLE SPREADS OF DATA.

COMPARING DISTRIBUTIONS

CHAPTER 6: THE STANDARD DEVIATION AS A RULER AND THE NORMAL MODEL

• STANDARD DEVIATION

• ANSWERS THE QUESTION HOW FAR IS THIS VALUE FROM THE MEAN AND HOW DIFFERENT ARE THESE TWO STATISTICS

• STANDARDIZED VALUES OR Z-SCORES MEASURE THE DISTANCE OF EACH DATA VALUE FROM THE MEAN IN STANDARD DEVIATIONS. STANDARDIZED VALUES HAVE NO UNITS.

• SHIFTING DATA

• WHEN WE ADD OR SUBTRACT A CONSTANT TO EACH VALUE ALL MEASURES OF POSITION(CENTER, PERCENTILES, MIN, AND MAX) WILL INCREASE OR DECREASE BY THAT SAME CONSTANT. THIS LEAVES SPREAD THE SAME.

• WHEN WE MULTIPLY OR DIVIDE BY A CONSTANT TO EACH VALUE ALL MEASURES OF POSITION AND SPREAD WILL BE MULTIPLIED OR DIVIDED BY THAT CONSTANT.

CHAPTER 6 CONT.• NORMAL MODEL

• THE BELL SHAPE CURVE THAT IT IS APPROPRIATE FOR DISTRIBUTIONS WHOSE SHAPES ARE UNIMODAL AND SYMMETRIC.

• NUMBERS WE USE TO SPECIFY THIS MODEL ARE CALLED PARAMETERS.

• SUMMARIES OF THIS DATA ARE CALLED STATISTICS.

• A NORMAL MODEL WITH A MEAN OF 0 AND A STANDARD DEVIATION OF 1 IS CALLED THE STANDARD NORMAL MODEL.

• IN ORDER TO USE THIS MODEL THE DATA MUST MEET THE NEARLY NORMAL CONDITION.

• THE 68-95-99.7 RULE- SAYS THAT 68% OF THE DATA WILL FALL WITHIN 1 STANDARD DEVIATION OF THE MEAN, 95% WILL FALL WITHIN 2 STANDARD DEVIATIONS, AND 99.7% WILL FALL WITHIN 3 STANDARD DEVIATIONS.

CHAPTER 6 CONT.

• RULES FOR WORKING WITH THE NORMAL MODEL

1. MAKE A PICTURE

2. MAKE A PICTURE

3. MAKE A PICTURE

• NORMAL PROBABILITY PLOT- TELLS YOU IF YOUR DATA IS NORMAL BY SHOWING WHETHER OR NOT YOUR DATA LIES ON A DIAGONAL LINE.

NORMAL MODEL AND NORMAL PROBABILITY PLOT