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Essentials of Statistics 3rd edition

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1 Essentials of Statistics 3rd edition
Introduction To Statistics Math 13 Essentials of Statistics 3rd edition by Mario F. Triola Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

2 Chapter 1 Introduction to Statistics
1-1 Overview 1-2 Types of Data 1-3 Critical Thinking 1-4 Design of Experiments

3 Section 1-1 Overview Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

4 Overview A common goal of studies and surveys is to collect data from a small part of a larger group so as to learn something about the larger group. That is what the science of statistics does: tells us how to: 1) collect data with an appropriate sample; 2) organize, analyze, and describe it; and 3) make inferences about the entire population based on the data collected.

5 You will learn about: Collecting data using different random sampling techniques; Analyzing data by taking different kinds of measurements of it to observe a pattern or trend; Inferring a hypothesis from the observed measurements; Verifying your hypothesis.

6 Definition Data bits of information collected through observations, measurements, survey responses. The set of the student heights, in inches, in our class is: {66, 64, 72, 69, 85, …}; The set of the student voting preferences in our class is: {democrat, democrat, republican, undecided,….} Singular for ‘Data’ is Datum, or Data Element, or Data Value.

7 Definition Population Census
the complete collection of all elements (scores, subjects, measurements, etc.) to be studied; the collection is complete in the sense that it includes all subjects to be studied: All American adults consume on average 20.5 lbs of sugar per year. All factory bearings have a lifetime warranty. Census collection of data from every member of a population. Virtually impossible thing to do. Very susceptive to errors.

8 Definition Sample Sub-set of members selected from a population:
A sample is easier to collect, but it must be random in order to have any statistical significance. The 1097 sampled adults consume on average 22 lbs of sugar per year.

9 Definition Parameter Statistic
measurement which describes the Population: In the statement “All American adults consume on average 20.5 lbs of sugar per year”, the number 20.5 is a parameter. Statistic measurement which describes the Sample: In the statement “the 1097 sampled adults consume on average 22 lbs of sugar per year’, the number 22 is a statistic.

10 Population Definition parameter sample statistic Parameter Statistic
a number that describes the Population: Population parameter Statistic a number that describes the Sample: sample statistic

11 Key Concepts Sample data must be representative of the entire population, which means it must be collected through a process of random selection in order to enable us to draw from this sample conclusions about the population. If sample data are not collected in an appropriate way, the data may be completely useless and the methods of statistics will not apply.

12 Key Concept If sample data are collected in an appropriate way, then we are interested in using the sample data to make inferences (or generalizations) about the entire population.

13 Section 1-2 Types of Data Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

14 DATA Numerical Categorical Discrete Continuous (Quantitative)
(Qualitative) Discrete numerical data come from measurements that can only be measured in a finite or countable number of ways, each of which has a clear boundary point on the number line. – COUNTS. Continuous numerical data come from measurements which can be measured in an infinite number of values; each measurement has no clear bounbdary with the next one. – PHYSICAL MEASUREMENTS. Discrete Continuous Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

15 Definition Numerical (Quantitative) data
are numbers representing counts or measurements. It makes sense to find the average of a set of numerical data: The weights of students; The number of cars per household; The blood type (?)

16 Definition Categorical (Qualitative) data
are symbols, names, numbers, letters representing different categories. It makes NO sense to find the average of a set of categorical data: The genders of students; The color of cars; The blood type.

17 DATA Numerical Categorical Discrete Continuous
(Quantitative) Categorical (Qualitative) Discrete Continuous DATA Numerical data can further be described as discrete or continuous.

18 Definition Discrete numerical data
come from observations that can only be measured in a finite (or countable) number of ways, each of which has a clear boundary point on the number line – counts: the number of cars in a household; the number of offspring an elephant produces; the salary of an adult, to the nearest dollar;

19 Definition Continuous numerical data
come from observations that can be measured in infinitely many possible values, which can be viewed on a continuous scale without gaps; each measurement has no clear boundary with the next one –measurements: The amount of milk that a cow produces; e.g gallons per day; The student’s height, if not rounded off.

20 DATA Numerical Categorical Discrete Continuous (Quantitative)
(Qualitative) Discrete Continuous DATA

21 Levels of Measurement Another way to classify data is to use levels of measurement. There are four of these levels: Nominal Ordinal Interval Ratio

22 Nominal level of measurement
Definition Nominal level of measurement are data that consist of categories only. Nominal data cannot be arranged in any order (such as low to high) Survey responses: yes, no, undecided Blood type: A, B, AB, O Car color: red, blue, silver, … Gender: male or female

23 Ordinal level of measurement
Definition Ordinal level of measurement are data that can be arranged in some order. Ordinal data allow for relative comparison. However differences between data values cannot be determined or are meaningless – difference comparison is impossible: Course grades: A, B, C, D, or F Class of a Hotel: 1st, 2nd, 3rd, … Gender: male or female (?)

24 Definition Interval level of measurement
are data which can be arranged in some order, with the additional property that the difference between any two data values is meaningful. Interval data allow for difference comparison. However, there is no natural zero starting point, which makes the ratio comparison impossible: Year of a masterpiece: 1000, 2000, 1998, etc. Body temperature: 101.2, 104.5, 103.0, … Test score: 70%, 85%, 94%, 50% (?)

25 Definition Ratio level of measurement
is like the interval level with the additional property that there is a natural zero starting point (zero indicates that none of the quantity is present), which makes ratio comparisons also meaningful: The price of a textbook: $100, $200, $120, … The number of eggs a hen lays: 6, 12, 1, 0, … The amount of milk a cow produces: 2.34, 3.11, etc gallons per day

26 Summary - Levels of Measurement
Nominal - categories only; no comparison is possible; Ordinal - categories (or numbers grouped in categories) arranged in order; relative comparison only; Interval – numbers; relative and difference comparison possible; Ratio – numbers; relative, difference and ratio comparison possible.

27 Recap In this section we have looked at:
Basic definitions and terms describing data Parameters versus statistics Types of data (quantitative and qualitative) Levels of measurement

28 QUIZZ

29 1. The population is A collection of observations. A collection of methods for planning studies and experiments. The complete collection of all elements. D. A sub-collection of members drawn from a larger group.

30 2. Which is an example of quantitative data?
A. Weights of high school students. B. Genders of actors and actresses. C. Colors of the rainbow. D. Consumer ratings of a particular automobile (below average, average, and above average.)

31 3. Which is not an example of continuous data?
A. Temperature on a thermometer. B. Number of students in an algebra class. C. Mean weight of 100 flour sacks. D. Amount of water pumped from a pond per day.

32 4. Questions on a survey are scored with integers 1 thru 5 with 1 representing Strongly Disagree and 5 Strongly Agree. This is an example of what kind of measurement? A. Nominal. B. Ratio. C. Ordinal. D. Interval.

33 5. Identify the level of measurement: the weights of people
A. Nominal. B. Ordinal. C. Interval. Ratio.

34 6. Identify the level of measurement: a movie critic’s classification of “drama”, “comedy”, “adventure”, “science-fiction” A. Nominal. B. Ordinal. C. Interval. Ratio.

35 7. Identify the level of measurement of the values “must see”, “recommend” and “don’t even think about going” which a movie critic is using to rate movies A. Nominal. B. Ordinal. C. Interval. Ratio.

36 ANSWER

37 The population is A collection of observations. A collection of methods for planning studies and experiments. The complete collection of all elements. D. A sub-collection of members drawn from a larger group.

38 The population is A collection of observations. A collection of methods for planning studies and experiments. The complete collection of all elements. D. A sub-collection of members drawn from a larger group.

39 Which is an example of quantitative data?
A. Weights of high school students. B. Genders of actors and actresses. C. Colors of the rainbow. D. Consumer ratings of a particular automobile (below average, average, and above average.)

40 Which is an example of quantitative data?
A. Weights of high school students. B. Genders of actors and actresses. C. Colors of the rainbow. D. Consumer ratings of a particular automobile (below average, average, and above average.)

41 Which is not an example of continuous data?
A. Temperature on a thermometer. B. Number of students in an algebra class. C. Mean weight of 100 flour sacks. D. Amount of water pumped from a pond per day.

42 Which is not an example of continuous data?
A. Temperature on a thermometer. B. Number of students in an algebra class. C. Mean weight of 100 flour sacks. D. Amount of water pumped from a pond per day.

43 Questions on a survey are scored with integers 1 thru 5 with 1 representing Strongly Disagree and 5 Strongly Agree. This is an example of what kind of measurement? A. Nominal. B. Ratio. C. Ordinal. D. Interval.

44 Questions on a survey are scored with integers 1 thru 5 with 1 representing Strongly Disagree and 5 Strongly Agree. This is an example of what kind of measurement? A. Nominal. B. Ratio. C. Ordinal. D. Interval.

45 Identify the level of measurement: the weights of people
A. Nominal. B. Ordinal. C. Interval. Ratio.

46 Identify the level of measurement of the variable weight
A. Nominal. B. Ordinal. C. Interval. Ratio.

47 Identify the level of measurement: a movie critic’s classification of “drama”, “comedy”, “adventure”, “science-fiction” A. Nominal. B. Ordinal. C. Interval. Ratio.

48 Identify the level of measurement: a movie critic’s classification of “drama”, “comedy”, “adventure”, “science-fiction” A. Nominal. B. Ordinal. C. Interval. Ratio.

49 Identify the level of measurement of the values “must see”, “recommend” and “don’t even think about going” which a movie critic is using to rate movies A. Nominal. B. Ordinal. C. Interval. Ratio.

50 Identify the level of measurement: a movie critic’s rating of “must see”, “recommend”, “don’t even think about going” A. Nominal. B. Ordinal. C. Interval. Ratio.

51 Any Queries ?


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