Describing Distributions Visually Section 1.1.1

Starter Problem Mr. McPeak plays a lot of golf. This summer he got a new driver and kept track of how far he hit his tee shots in several rounds. Look at these data (drive lengths in yards) and then write a few sentences that describe the lengths of his drives:

Today’s Objectives State whether a variable is categorical or quantitative. Manually create a dotplot and a histogram that represent given data. Describe a distribution in terms of center, spread and shape. California Standard 14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and- whisker plots.

Individuals and Variables Individuals are the objects described in data. –They MAY be people, but could be things. –Notice that for the golf tee shots, the “individuals” were the shots, each of which had its own length. Variables are the characteristics of interest in an individual. –Different individuals can have different values of a variable (such as hair color or height). –For the tee shots, the variable was the length the ball went after being hit.

Types of Variables Categorical variables record which group or category an individual belongs to. –What color is your hair? –What year are you in school? –What city do you live in? –Did the tee shot land in the fairway? –It does NOT make sense to average the results. Quantitative variables take on numeric values. –How tall is a person? –What score did a person get on the SAT? –How many desks are in a room? –How long was the tee shot? –It DOES make sense to average the results.

Visual Representation of Categorical Variables Categorical variables are typically represented by pie charts (for percents) or bar charts (percents or counts). Married?Count (M)Percent Single Married Widowed Divorced

Visual representation of Quantitative Variables: Dotplots The most basic method is a dotplot. –Every data point can be seen on the plot. Construction method: –Draw a horizontal axis with a scale that covers the full range of values for the variable. –Put a dot on (or above) the axis for each data point. –If data duplicate, stack them vertically. Construct a dotplot now of Mr. McPeak’s drives:

Dotplot of Drive Data Based on the dotplot, estimate the center. –We see it around 230 or 240 yards. Estimate the spread. –Roughly from 190 to almost 280, so spread is about 90 yards. Describe the shape. –It appears “mound-shaped” with most of the data clustered at the center and with tails at each end.

Visual representation of Quantitative Variables: Histograms Another important method is a histogram. –Individual data points cannot be seen on the plot. –Many data points are grouped together in vertical bars. Construction method: –Draw a horizontal axis with a scale that covers the full range of values for the variable. –Decide bar width (also called class width) so that 5 to 10 bars will cover the full range of data. –Set borders for bars, count frequencies, draw bars. –Use a vertical axis to show the bar height. Construct a histogram now for Mr. McPeak’s drives. –Use bars 10 yards wide, starting at 190 yards. –So bar borders will be 190, 200, 210, … etc. –Notice that your dotplot has all individual data points.

Histogram of Drive Data From a visual examination, estimate the center and spread; also describe the shape. –As before, you should see the center around 230 to 240, the spread looks like 90, and the shape still looks like a mound.

Today’s Objectives State whether a variable is categorical or quantitative. Manually create a dotplot and a histogram that represent given data. Describe a distribution in terms of center, spread and shape. California Standard 14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and- whisker plots.

Homework Read pages 4-15 in the text. –Ignore Activity 1. –Work through Example 1.2 in detail; pay attention to the calculator instruction. –Vocabulary and important concepts are highlighted by “boxing” them. There are five such cases in this assignment and there will be a quiz tomorrow! Do problems (exercises) 2 – 7. –Notice the first problem is 1.2 on page 8 –Respond fully to each question. One of them will be scored for your daily homework grade! –Use flat 3-ring binder filler paper or graph paper Use of spiral-bound paper with rough edges will lose points!