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Chapter 1: Section 2-4 Variables and types of Data.

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1 Chapter 1: Section 2-4 Variables and types of Data

2 Section 2: Types of Variables Qualitative Variables: Variables that can be placed into distinct categories, according to some characteristic or attribute. Ex: Gender, Eye color, Geographic Location

3 2 Types of Variables Quantitative Variables: Variables that are numerical and can be ordered or ranked. Ex: Age, height, weight, body temp Classified by two groups Discrete Variables Continuous Variables

4 Discrete Variables Assume values that can be counted Assigned numbers such as 0,1,2,3,… Ex: # of children # of students

5 Continuous Variables Can assume an infinite number of values between any two specific values. Obtained by measuring Often include fractions and decimals. Ex: Temperature Time Length

6 Measurement Scale Used to categorize, count, or measure variables. Types: Nominal Ordinal Interval Ratio

7 Nominal Level of Measurement Classifies data into mutually exclusive, exhausting categories in which no order or ranking can be imposed on the data. Ex: Male/Female Single/Married/Divorced/Widowed/Separated Democratic/Republican

8 Ordinal Level of Measurement Classifies data into categories that can be ranked; however, precise differences between the ranks do not exist. Ex: Letter Grades (A, B, C, D, F) 1 st, 2 nd, 3 rd, etc Small, Medium, Large Freshman, Sophomores, Juniors, Seniors

9 Interval Level of Measurement Ranks data, and precise differences between units of measures do exist: however, there is no meaningful zero. Ex: Temperature: 72°F and 73°F, difference of 1°F, but 0°F does not mean no heat present IQ: 109 and 110, difference of 1 point, but 0 does not mean there is no intelligence.

10 Ratio Level of Measurement Possesses all the characteristics of interval measurements, and there exists a true zero. In addition, true ratios exists when the same variables is measured on two different members of the population. Ex: Salary Time Age

11 Checking for Understanding “Applying the Concepts” page 9, # 1-6.

12 Section 3: Data Collection and Sampling Techniques. Types: Random Systematic Stratified Cluster

13 Random Sampling Selection based on chance or random numbers. Procedure: Assign number to each subject in population Select numbers at random from “hat”

14 Random Sampling 12 34567 89 1011121314 1516 1718192021

15 Systematic Sampling Procedure: Number each subject in population Select every kth subject Example: Population: 100 Sample: 10 Kth term: 100/10=10 1, 11, 21, 31, 41, 51, 61, 71, 81, 91

16 Systematic Sampling Population: 21 Sample: 7 21/7=3: kth term is 3. 12 34567 89 1011121314 1516 1718192021

17 Stratified Sampling Procedures: Population divided into groups called: Strata Groups have common characteristic needed for study. Samples randomly selected from each strata

18 Stratified Sampling

19 Cluster Sampling Population is divided into groups called: Clusters Select some clusters Survey every member of the cluster for sample Used with large populations

20 Cluster Sampling

21 Other sampling methods Convenience sampling Use subjects that are convent Ex: asking people as they enter the mall Sequential sampling Double sampling Multistage sampling

22 Convenience Sampling Do you want to take a survey?

23 Practice Page 26-27 #’s 6, 7, 8, 9, 11, 12

24 Section 4: 2 Types of Studies Observational Study Researchers merely observe what is happening or what has happened in the past Try to draw conclusions based on these observations. Ex: studying creatures in the wild “Meerkat Manor”

25 Experimental study Researchers manipulate one of the variables Tries to determine how to the manipulation influences other variables. Ex: New medication and placebos Section 4: 2 Types of Studies

26 Statistical Studies include…. Independent variables In an experimental study is the one that is being manipulated by the researcher. Also called: Explanatory variable Dependent variables Resultant variable Also called: Outcome variable

27 Misuses of Statistics Suspect Samples Too small Convenience Volunteers Changing the subject Increase of 3% Increase of $600,000

28 Detached Statistics- no comparison “Works 5 times faster” “1/3 fewer calories” Implied Connection “Eating fish may help you achieve better in school” Misuses of Statistics

29 Misleading Graphs- Chapter 2 Faulty Survey Questions “Do you feel there should be a 4 day school week?” “Do you feel there should be a 4 day school week from 4 am to midnight?” Misuses of Statistics

30 Section 1-6: Computers and Calculators Computer and Calculators GOOD

31 End of Chapter 1


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