Stat 20: Intro to Probability and Statistics
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1 Stat 20: Intro to Probability and Statistics Lecture 4: Data Displays (cont.) Tessa L. Childers-Day UC Berkeley 26 June 2014
2 By the end of this lecture... You will be able to: Comprehend displays of quantitative data Construct a histogram 2 / 18
3 Example: High School Hobbies (Hypothetical:) Imagine we are interested in exploring what kinds of hobbies high school students have below. We construct a survey: (1) Circle your gender: Female Male (2) Circle your class level: Fresh Soph Jr Sr (3) What is your GPA ( )? (4) What is your height in inches? (5) What is your weight in pounds? (6) What is your favorite hobby? 3 / 18
4 Example: High School Hobbies (cont.) A selection of the hypothetical raw data appear below: obs gender class level gpa height weight hobbies 1 male jr watching tv 2 female soph facebook 3 female jr baseball 4 male jr soccer 5 male sr yearbook 6 female jr baseball 7 male sr facebook 8 female fresh gymnastics 9 male sr hanging out 10 male jr reading 4 / 18
5 Ways to classify data Level of Measurement: Qualitative Nominal Ordinal Quantitative Interval Ratio Countability: Discrete Continuous 5 / 18
6 Displaying Qualitative Data Helps to summarize/organize raw data visually Data Tables Distribution Tables Contingency Tables Pie Charts Bar Charts Word Clouds How can we make this work for quantitative data as well? 6 / 18
7 Quantitative Data Displays Today: Quantitative Data Stem and Leaf Plot Scatterplot Histogram Frequency Density Smoothed Histogram Will not work for qualitative data 7 / 18
8 Stem and Leaf Plot A stem and leaf plot breaks the numbers into groups/classes, usually based on the first (several) digits. This is the stem. The last digit is the leaf. The data gets sorted, and each data point gets put onto a leaf. GPA stem leaf ones tenths What is good about this display? What is bad? 8 / 18
9 Scatterplots A scatterplot represents each data point by a dot, and plots the dots on a pair of axes Height of High Schoolers Observation Height (inches) Height of High Schoolers Rank Height (inches) 9 / 18
10 Scatterplots (cont.) Here we have two data types plotted together Plot the pair (x,y) = (height, weight) for each student But we say we ve plotted y vs. x or weight vs. height or weight against height Weight vs. Height of High Schoolers Height (inches) Weight (pounds) What is good about this display? What is bad? 10 / 18
11 Histogram A histogram is like a bar chart, but is intended for quantitative data, instead of qualitative data. Data broken into mutually exclusive, exhaustive classes Numerically adjoining classes are connected Need to know the endpoint convention Pretends data is spread evenly over class interval 11 / 18
12 Histogram (cont.) Frequency Histogram Height represents frequency of observations which fall into each class Sum of all frequencies = total number of observations Class widths are equal just compare heights/frequencies Frequency Histogram of Weight of High Schoolers Weight (pounds) 12 / 18
13 Histogram (cont.) Density Histogram Area represents the percentage of data in a class Histogram of Weight of High Schoolers area = base height = percentage height = percentage base = % per unit of x = density Height represents density (crowding) of observations in each class Density (% per pound) Weight (pounds) 13 / 18
14 Histogram (cont.) Density Histogram Total area = 100% If class widths equal, compare heights percentage in a class = density class width Can add percentages No fixed number of classes Density (% per pound) Histogram of Weight of High Schoolers Weight (pounds) 14 / 18
15 Histogram (cont.) Histogram of Weight of High Schoolers Histogram of Weight of High Schoolers Density (% per pound) Density (% per pound) Weight (pounds) Weight (pounds) What is good about this kind of display? What is bad? 15 / 18
16 Smoothed Histogram With the advent of computers, it became possible to smooth a histogram (estimate a density) Smoothed Histogram Basically take class width to zero Total area = 100% Smooths histogram to reflect continuity of data Have to pick bandwidth (amount of smoothing) Doesn t pretend data is spread evenly over class interval Density (% per pound) Smoothed Histogram of Weight of High Schoolers Weight (pounds) 16 / 18
17 Smoothed Histogram (cont.) Smoothed Histogram of Weight of High Schoolers Smoothed Histogram of Weight of High Schoolers Density (% per pound) Density (% per pound) Weight (pounds) What is good about this display? What is bad? Weight (pounds) 17 / 18
18 Important Takeaways Need to display data hard to understand raw data, especially in large amounts Quantitative Data Displays Stem and Leaf Plot Scatterplot Histogram (frequency and density) Smoothed Histogram Next time: Summary Statistics 18 / 18
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