Unit 1 - Graphs and Distributions

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

Descriptive statistics the methods of organizing & summarizing data

Inferential statistics involves making generalizations from a sample to a population

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

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

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

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

Types of variables

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

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

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

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

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

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

Types of Distributions 4 common types

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

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

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

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

Dotplots Stem & leaf plots Histograms Boxplots How to describe a graph Dotplots Stem & leaf plots Histograms Boxplots Do after Features of Distributions Activity

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

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

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

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

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