Basic Practice of Statistics - 5th Edition Chapter 1 Picturing Distributions with Graphs BPS - 5th Ed. Chapter 1 Chapter 1

Basic Practice of Statistics - 5th Edition Statistics is a science that involves the extraction of information from numerical data obtained during an experiment or from a sample. It involves the design of the experiment or sampling procedure, the collection and analysis of the data, and making inferences (statements) about the population based upon information in a sample. BPS - 5th Ed. Chapter 1 Chapter 1

Data: typically, a collection of the values of the variables BPS - 5th Ed. Chapter 1

Individuals and Variables Basic Practice of Statistics - 5th Edition Individuals and Variables Individuals the objects described by a set of data may be people, animals, or things Variable any characteristic of an individual can take different values for different individuals BPS - 5th Ed. Chapter 1 Chapter 1

Basic Practice of Statistics - 5th Edition Variables/Data Categorical Places an individual into one of several groups or categories Quantitative (Numerical) Takes numerical values for which arithmetic operations such as adding and averaging make sense BPS - 5th Ed. Chapter 1 Chapter 1

Case Study BPS - 5th Ed. Chapter 1

Case Study The Effect of Hypnosis on the Immune System reported in Science News, Sept. 4, 1993, p. 153 BPS - 5th Ed. Chapter 1

Case Study The Effect of Hypnosis on the Immune System Objective: To determine if hypnosis strengthens the disease-fighting capacity of immune cells. BPS - 5th Ed. Chapter 1

Case Study 65 college students. white blood cell counts measured 33 easily hypnotized 32 not easily hypnotized white blood cell counts measured all students viewed a brief video about the immune system. BPS - 5th Ed. Chapter 1

Case Study Students randomly assigned to one of three conditions subjects hypnotized, given mental exercise subjects relaxed in sensory deprivation tank control group (no treatment) BPS - 5th Ed. Chapter 1

Case Study white blood cell counts re-measured after one week the two white blood cell counts are compared for each group results hypnotized group showed larger jump in white blood cells “easily hypnotized” group showed largest immune enhancement BPS - 5th Ed. Chapter 1

Case Study Variables measured Easy or difficult to achieve hypnotic trance Group assignment Pre-study white blood cell count Post-study white blood cell count categorical quantitative BPS - 5th Ed. Chapter 1

Case Study BPS - 5th Ed. Chapter 1

Case Study Weight Gain Spells Heart Risk for Women “Weight, weight change, and coronary heart disease in women.” W.C. Willett, et. al., vol. 273(6), Journal of the American Medical Association, Feb. 8, 1995. (Reported in Science News, Feb. 4, 1995, p. 108) BPS - 5th Ed. Chapter 1

Case Study Weight Gain Spells Heart Risk for Women Objective: To recommend a range of body mass index (a function of weight and height) in terms of coronary heart disease (CHD) risk in women. BPS - 5th Ed. Chapter 1

Case Study Study started in 1976 with 115,818 women aged 30 to 55 years and without a history of previous CHD. Each woman’s weight (body mass) was determined. Each woman was asked her weight at age 18. BPS - 5th Ed. Chapter 1

Case Study The cohort of women were followed for 14 years. The number of CHD (fatal and nonfatal) cases were counted (1292 cases). BPS - 5th Ed. Chapter 1

Case Study Variables measured quantitative Age (in 1976) Weight in 1976 Weight at age 18 Incidence of coronary heart disease Smoker or nonsmoker Family history of heart disease categorical BPS - 5th Ed. Chapter 1

Distribution BPS - 5th Ed. Chapter 1

Distribution Tells what values a variable takes and how often it takes these values Can be a table, graph, or function BPS - 5th Ed. Chapter 1

Displaying Distributions Categorical variables Pie charts Bar graphs Quantitative variables Histograms Stemplots (stem-and-leaf plots) BPS - 5th Ed. Chapter 1

Class Make-up on First Day Data Table Year Count Percent Freshman 18 41.9% Sophomore 10 23.3% Junior 6 14.0% Senior 9 20.9% Total 43 100.1% BPS - 5th Ed. Chapter 1

Class Make-up on First Day Pie Chart BPS - 5th Ed. Chapter 1

Class Make-up on First Day Basic Practice of Statistics - 5th Edition Class Make-up on First Day Bar Graph BPS - 5th Ed. Chapter 1 Chapter 1

Example: U.S. Solid Waste (2000) Basic Practice of Statistics - 5th Edition Example: U.S. Solid Waste (2000) Data Table Material Weight (million tons) Percent of total Food scraps 25.9 11.2 % Glass 12.8 5.5 % Metals 18.0 7.8 % Paper, paperboard 86.7 37.4 % Plastics 24.7 10.7 % Rubber, leather, textiles 15.8 6.8 % Wood 12.7 Yard trimmings 27.7 11.9 % Other 7.5 3.2 % Total 231.9 100.0 % BPS - 5th Ed. Chapter 1 Chapter 1

Example: U.S. Solid Waste (2000) Basic Practice of Statistics - 5th Edition Example: U.S. Solid Waste (2000) Pie Chart BPS - 5th Ed. Chapter 1 Chapter 1

Example: U.S. Solid Waste (2000) Basic Practice of Statistics - 5th Edition Example: U.S. Solid Waste (2000) Bar Graph BPS - 5th Ed. Chapter 1 Chapter 1

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Examining the Distribution of Quantitative Data Basic Practice of Statistics - 5th Edition Examining the Distribution of Quantitative Data Overall pattern of graph Deviations from overall pattern Shape of the data Center of the data Spread of the data (Variation) Outliers BPS - 5th Ed. Chapter 1 Chapter 1

Basic Practice of Statistics - 5th Edition Shape of the Data Symmetric bell shaped other symmetric shapes Asymmetric right skewed left skewed Unimodal, bimodal BPS - 5th Ed. Chapter 1 Chapter 1

Symmetric Bell-Shaped Basic Practice of Statistics - 5th Edition Symmetric Bell-Shaped BPS - 5th Ed. Chapter 1 Chapter 1

Symmetric Mound-Shaped Basic Practice of Statistics - 5th Edition Symmetric Mound-Shaped BPS - 5th Ed. Chapter 1 Chapter 1

Basic Practice of Statistics - 5th Edition Symmetric Uniform BPS - 5th Ed. Chapter 1 Chapter 1

Asymmetric Skewed to the Left Basic Practice of Statistics - 5th Edition Asymmetric Skewed to the Left BPS - 5th Ed. Chapter 1 Chapter 1

Asymmetric Skewed to the Right Basic Practice of Statistics - 5th Edition Asymmetric Skewed to the Right BPS - 5th Ed. Chapter 1 Chapter 1

Outliers BPS - 5th Ed. Chapter 1

BPS - 5th Ed. Chapter 1

Basic Practice of Statistics - 5th Edition Outliers Extreme values that fall outside the overall pattern May occur naturally May occur due to error in recording May occur due to error in measuring Observational unit may be fundamentally different BPS - 5th Ed. Chapter 1 Chapter 1

Histograms BPS - 5th Ed. Chapter 1

Histograms For quantitative variables that take many values Divide the possible values into class intervals (we will only consider equal widths) Count how many observations fall in each interval (may change to percents) Draw picture representing distribution BPS - 5th Ed. Chapter 1

Histograms: Class Intervals How many intervals? One rule is to calculate the square root of the sample size, and round up. Size of intervals? Divide range of data (maxmin) by number of intervals desired, and round to convenient number Pick intervals so each observation can only fall in exactly one interval (no overlap) BPS - 5th Ed. Chapter 1

Basic Practice of Statistics - 5th Edition Case Study Weight Data Introductory Statistics class Spring, 1997 Virginia Commonwealth University BPS - 5th Ed. Chapter 1 Chapter 1

Weight Data BPS - 5th Ed. Chapter 1

Weight Data: Frequency Table Basic Practice of Statistics - 5th Edition Weight Data: Frequency Table sqrt(53) = 7.2, or 8 intervals; range (260100=160) / 8 = 20 = class width BPS - 5th Ed. Chapter 1 Chapter 1

Weight Data: Histogram Basic Practice of Statistics - 5th Edition Weight Data: Histogram Number of students 100 120 140 160 180 200 220 240 260 280 Weight * Left endpoint is included in the group, right endpoint is not. BPS - 5th Ed. Chapter 1 Chapter 1

Stemplots BPS - 5th Ed. Chapter 1

Stemplots (Stem-and-Leaf Plots) For quantitative variables Separate each observation into a stem (first part of the number) and a leaf (the remaining part of the number) Write the stems in a vertical column; draw a vertical line to the right of the stems Write each leaf in the row to the right of its stem; order leaves if desired BPS - 5th Ed. Chapter 1

Weight Data 1 2 BPS - 5th Ed. Chapter 1

Weight Data: Stemplot (Stem & Leaf Plot) Basic Practice of Statistics - 5th Edition 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Weight Data: Stemplot (Stem & Leaf Plot) 192 5 152 2 135 Key 20|3 means 203 pounds Stems = 10’s Leaves = 1’s 2 The student should construct a stem & leaf plot here using the first two digits as the stem and the last digit as the leaf. The shape of the stem & leaf plot should look similar to the bar graph shown on an upcoming slide. BPS - 5th Ed. Chapter 1 Chapter 1

Weight Data: Stemplot (Stem & Leaf Plot) Basic Practice of Statistics - 5th Edition 10 0166 11 009 12 0034578 13 00359 14 08 15 00257 16 555 17 000255 18 000055567 19 245 20 3 21 025 22 0 23 24 25 26 0 Weight Data: Stemplot (Stem & Leaf Plot) Key 20|3 means 203 pounds Stems = 10’s Leaves = 1’s The student should construct a stem & leaf plot here using the first two digits as the stem and the last digit as the leaf. The shape of the stem & leaf plot should look similar to the bar graph shown on an upcoming slide. BPS - 5th Ed. Chapter 1 Chapter 1

Extended Stem-and-Leaf Plots If there are very few stems (when the data cover only a very small range of values), then we may want to create more stems by splitting the original stems. BPS - 5th Ed. Chapter 1

Extended Stem-and-Leaf Plots Example: if all of the data values were between 150 and 179, then we may choose to use the following stems: 15 15 16 16 17 17 Leaves 0-4 would go on each upper stem (first “15”), and leaves 5-9 would go on each lower stem (second “15”). BPS - 5th Ed. Chapter 1

Time Plots BPS - 5th Ed. Chapter 1

Time Plots A time plot shows behavior over time. Time is always on the horizontal axis, and the variable being measured is on the vertical axis. Look for an overall pattern (trend), and deviations from this trend. Connecting the data points by lines may emphasize this trend. Look for patterns that repeat at known regular intervals (seasonal variations). BPS - 5th Ed. Chapter 1

Class Make-up on First Day (Fall Semesters: 1985-1993) BPS - 5th Ed. Chapter 1

Average Tuition (Public vs. Private) BPS - 5th Ed. Chapter 1