Unit 1 - Graphs and Distributions

Statistics 4 the science of collecting, analyzing, and drawing conclusions from data

Descriptive statistics 4 the methods of organizing & summarizing data

Inferential statistics 4 involves making generalizations from a sample to a population

ASK??? 4 Who? –What individuals…. –How many ….. 4 What? –Variables… –Exact definitions… –Units 4 Why?

Population 4 The entire collection of individuals or objects about which information is desired

Sample 4 A subset of the population, selected for study in some prescribed manner

Variable 4 any characteristic whose value may change from one individual to another

Data 4 observations on single variable or simultaneously on two or more variables

Types of variables

Categorical variables 4 or Qualitative variables 4 identifies basic, differentiating characteristics of the population

Numerical variables 4 or Quantitative variables 4 observations or measurements take on numerical values 4 makes sense to average these values 4 two types - discrete & continuous

Problem 1.1 Page 7 4 What are the individuals in this data set? 4 For each individual, what variables are given? Which of these variables are categorical and which are quantitative?

Discrete (Numerical) 4 listable set of values 4 usually counts of items

Continuous (Numerical) 4 data can take on any values in the domain of the variable 4 usually measurements of something

Classification by the number of variables 4 Univariate - data that describes a single characteristic of the population 4 Bivariate - data that describes two characteristics of the population 4 Multivariate - data that describes more than two characteristics (beyond the scope of this course

Identify the following: 4 gender 4 age 4 hair color 4 smoker 4 systolic blood pressure 4 number of girls in class 4 categorical 4 numerical 4 categorical 4 numerical

Types of Graphs 4 Bar Graph – pg 9 4 Pie Charts – pg 9 4 Dotplots – pg 11 4 Stem & Leaf – pg 13 4 Histogram – pg 19 4 Time plot – pg 31 4 Box & Whisker – pg Categorical Variables

Problem 1.8 (a) page 17

Caffeine Content (mg) per 8-ounce serving of various soft drinks Key: 3|5 means the soft drink contains 35 mg of caffeine per 8-ounce serving.

Caffeine Content (mg) per 8-ounce serving of various soft drinks Key: 3|5 means the soft drink contains 35 mg of caffeine per 8-ounce serving.

Types of Distributions 4 common types

4 Distribution – tells us what values the variable takes and how often it takes the values.

Symmetrical 4 refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle 4 bell-shaped is a special type –has a center mound with two sloping tails

Uniform 4 refers to data in which every class has equal or approximately equal frequency

Skewed (left or right) 4 refers to data in which one side (tail) is longer than the other side 4 the direction of skewness is on the side of the longer tail

Bimodal (multi-modal) 4 refers to data in which two (or more) classes have the largest frequency & are separated by at least one other class

How to describe a graph Dotplots Stem & leaf plots Histograms Boxplots

1. Center 4 discuss where the middle of the data falls 4 three types of central tendency –mean, median, & mode

2. Spread 4 discuss how spread out the data is 4 refers to the variability of the data –Range, standard deviation, IQR

3. Shape of the Distribution 4 refers to the overall type of the distribution 4 symmetrical, uniform, skewed, or bimodal

4. Unusual occurrences 4 outliers - value that lies away from the rest of the data 4 gaps 4 clusters 4 anything else unusual

5. In context 4 You must write your answer in reference to the specifics in the problem, using correct statistical vocabulary and using complete sentences!