Introduction to Statistics PDF

QUARTER 2: Research 8 Introduction to Statistics INTRODUCTION TO STATISTICS Statistics Statistics is the study of collecting, organizing, and interpreting data. In everyday life, we use statistics to make decisions based on numbers and information. This module...

QUARTER 2: Research 8 Introduction to Statistics INTRODUCTION TO STATISTICS Statistics Statistics is the study of collecting, organizing, and interpreting data. In everyday life, we use statistics to make decisions based on numbers and information. This module will help you understand the basic terms, scales of measurement, and the mathematical symbols used in statistics. A. Definition of Terms in Statistics Here are some key terms in statistics: 1. Data Definition: Data is a collection of facts or information. It can be numbers, words, measurements, or observations. Example: The ages of students in your class or the number of books in a library. 2. Population Definition: A population is the entire group of individuals or items you are studying. Example: All the students in your school. 3. Sample Definition: A sample is a smaller group taken from the population to represent the whole population. Example: The students in one class chosen to represent the whole school. 4. Variable Definition: A variable is a characteristic or property that can change or vary. Example: The height, weight, or age of people. 5. Frequency Definition: Frequency is the number of times a particular data value appears. Example: If 5 students in your class are 12 years old, then the frequency of the number 12 is 5. Key Differences in a Table Term Definition Example A collection of information, such as Test scores, ages of students, Data numbers, words, or measurements. colors of cars. All the students in your school, Population The entire group you are studying. all the books in a library. Theresa G. Dangkulos CLTL-University Science High School QUARTER 2: Research 8 Introduction to Statistics Term Definition Example A smaller group taken from the A class of students from a school, Sample population to represent the whole. 10 books selected from a library. A characteristic or property that can Height, age, favorite color, shoe Variable change. size. The number of times a data value How many times the number 12 Frequency appears in a set. appears in the list of ages. CHECKPOINT! Check Your Understanding Choose the letter of the correct answer: 1. What is the definition of data? a) A collection of facts or information b) A sample of a population c) A type of graph used to organize data d) A measure of central tendency 2. Which of the following is an example of a population? a) The students in a single class b) All the students in a school c) A group of students chosen to represent the whole school d) The test scores of five students 3. What is a sample? a) The entire group being studied b) A smaller group chosen to represent the population c) The average of a data set d) A type of data that cannot change 4. What is a variable? a) A characteristic that does not change b) A characteristic that can change or vary c) The total of all data values d) The frequency of a data point Theresa G. Dangkulos CLTL-University Science High School QUARTER 2: Research 8 Introduction to Statistics 5. What does frequency refer to? a) The average value in a data set b) The number of times a particular data value appears c) The difference between the highest and lowest values d) The middle value in a data set Answer Key a) A collection of facts or information b) All the students in a school b) A smaller group chosen to represent the population b) A characteristic that can change or vary b) The number of times a particular data value appears B. Scales of Measurement In statistics, we measure data using different types of scales. The scale you use depends on what type of data you are working with. There are four basic scales of measurement: 1. Nominal Scale Definition: This scale is used for categorizing data without any order. The data values are just labels or names. Examples: Types of Animals: Dog, Cat, Rabbit, Fish (These are simply categories without any order. You can't say one animal is "greater" than another.) Colors of Cars: Red, Blue, Green, Black (Colors are labels that have no inherent order. They are just different categories.) Favorite Ice Cream Flavors: Vanilla, Chocolate, Strawberry (These are just names. There's no ranking or measurement between them.) 2. Ordinal Scale Definition: This scale is used for data that can be ordered or ranked, but the differences between the ranks are not equal. Theresa G. Dangkulos CLTL-University Science High School QUARTER 2: Research 8 Introduction to Statistics Examples: Ranks in a Race: 1st place, 2nd place, 3rd place (You can rank the places, but the difference between 1st and 2nd place isn’t necessarily the same as between 2nd and 3rd.) Survey on Satisfaction: Very Satisfied, Satisfied, Neutral, Dissatisfied, Very Dissatisfied (These are ordered from most to least satisfied, but the difference between each level is not the same.) Movie Ratings: Excellent, Good, Fair, Poor (These show an order, but the difference in quality between each rating is subjective and not exactly measurable.) 3. Interval Scale Definition: This scale is used for data with ordered values where the difference between values is meaningful, but there is no true zero point. Examples: Temperature (Celsius or Fahrenheit): 10°C, 20°C, 30°C (The difference between 10°C and 20°C is the same as between 20°C and 30°C. However, 0°C does not mean there is "no temperature" – it's just a reference point.) Time on a 24-hour clock: 3:00 PM, 6:00 PM, 9:00 PM (The difference in time is meaningful, but 12:00 AM does not mean "no time.") 4. Ratio Scale Definition: This scale is similar to the interval scale, but it has a true zero point. Ratios between values are meaningful. Examples: Height: 0 cm, 50 cm, 100 cm (Zero means no height, and the ratios between values make sense – a person 100 cm tall is twice as tall as a person 50 cm tall.) Weight: 0 kg, 20 kg, 60 kg (Zero weight means no weight, and the ratios are meaningful – a person weighing 60 kg weighs three times more than someone who weighs 20 kg.) Theresa G. Dangkulos CLTL-University Science High School QUARTER 2: Research 8 Introduction to Statistics Distance: 0 meters, 5 meters, 10 meters (Zero meters means no distance, and the distance between values is meaningful, so 10 meters is twice the distance of 5 meters.) Key Differences in a Table Scale Type Characteristics Examples Nominal Categories, no order or ranking Animals, Colors, Flavors Ordered, but differences are not Ranks, Movie Ratings, Survey Ordinal meaningful Results Interval Ordered, equal intervals, no true zero Temperature, Time Ratio Ordered, equal intervals, true zero Height, Weight, Distance CHECKPOINT! Check Your Understanding Choose the letter of the correct answer. 1. Which scale of measurement involves data that can be ordered and has a meaningful zero point? a) Nominal b) Ordinal c) Interval d) Ratio 2. Which of the following is an example of data measured on a nominal scale? a) The ranking of students in a race b) The color of shirts worn by students in a class c) The temperature in degrees Celsius d) The time taken to finish a test Theresa G. Dangkulos CLTL-University Science High School QUARTER 2: Research 8 Introduction to Statistics 3. Which scale of measurement allows you to compare the differences between values, but doesn’t have a true zero? a) Nominal b) Ordinal c) Interval d) Ratio 4. The number of students in a classroom is an example of data measured on which scale? a) Nominal b) Ordinal c) Interval d) Ratio 5. Which of the following is an example of data measured on an ordinal scale? a) Temperature measured in degrees Celsius b) Ranking of students in a class based on grades c) The number of students in each grade level d) The colors of cars in a parking lot Answer Key: d) Ratio b) The color of shirts worn by students in a class c) Interval d) Ratio b) Ranking of students in a class based on grades Key Summary of this Module Statistics is the study of collecting, organizing, analyzing, interpreting, and presenting data. It helps in making decisions based on data. Key Terms: Data: A collection of facts or information (e.g., ages, test scores). Population: The entire group being studied (e.g., all students in a school). Sample: A smaller group from the population, selected for study (e.g., students from one class). Variable: A characteristic that can change or vary (e.g., height, weight). Theresa G. Dangkulos CLTL-University Science High School QUARTER 2: Research 8 Introduction to Statistics Frequency: The number of times a particular data value appears. Scales of Measurement: Nominal Scale: Data categorized without order (e.g., types of animals). Ordinal Scale: Data ordered, but differences between ranks aren’t meaningful (e.g., rankings in a race). Interval Scale: Data ordered with meaningful differences, but no true zero (e.g., temperature in Celsius). Ratio Scale: Data with ordered values, meaningful differences, and a true zero (e.g., height, weight). Theresa G. Dangkulos CLTL-University Science High School