Collecting and Organizing Data PDF

# Statistics - Statistics is a branch of mathematics that involves collecting, organizing, analyzing, and interpreting data to help us make informed decisions. - Data refers to information such as facts and numbers used to analyze something or to make a decision. - Data can come in various forms, s...

# Statistics - Statistics is a branch of mathematics that involves collecting, organizing, analyzing, and interpreting data to help us make informed decisions. - Data refers to information such as facts and numbers used to analyze something or to make a decision. - Data can come in various forms, such as numbers, words, measurements, or observations, and it often used to gain insights, answer questions, or solve a problem. ## Importance of Data - **Helps Us Make Decisions** - Data provides the information we need to make better choices. - For example, PAGASA provides weather forecasts to help people make decisions about their daily activities. - **Reveals Patterns and Trends** - Data allows us to see what happens often or changes over time. - For example, a sports team might notice that they perform better in games after a particular type of practice. - **Supports Fairness and Accuracy** - Data ensures decisions are based on facts, not guesses. - For example, Fake news spreads false information, but accurate data helps us uncover the truth. - **Solves Problems** - Data helps us find solutions by understanding the problem better. - For example, a city might use traffic data to decide where to build a new road to reduce congestion. - **Used Everywhere** - Data is essential in school, business, medicine, sports, and technology. - For example, doctors use medical data to diagnose illnesses, while companies use sales data to improve their products. # Types of Data - **Qualitative Data** - Describes qualities, characteristics, or categories and cannot be measured in numbers. - Answers questions like "What kind?" or "Which type?" - Examples: - Favorite colors of students (e.g., red, blue) - Types of pets (e.g., dog, cat, bird) - Levels of satisfaction (e.g., satisfied, neutral, dissatisfied) - **Quantitative Data** - Represents quantities or amounts and can be measured or counted. - Is always numerical and answers questions like "How many?" or "How much?" - Examples: - Height of students in centimeters - Number of books on a shelf - Temperature in degrees Celsius # Identifying Qualitative and Quantitative Data - Identifying the color of each car in the parking lot. **Qualitative** - Determining the number of students in each class. **Quantitative** - Rating a movie as "excellent", "good", or "poor". **Qualitative** - Describing the taste of different ice cream flavors. **Qualitative** - Counting the total pages in a book. **Quantitative** # Exercise A For each scenario or statement below, identify whether the data provided is qualitative (L) or quantitative (N). 1. Identifying the color of each car in the parking lot **L** 2. Determining the number of students in each class **N** 3. Rating a movie as “excellent”, “good”, or “poor” **L** 4. Recording the grades of students in a mathematics exam **N** 5. Describing the taste of different ice cream flavors **L** 6. Counting the total pages in a book **N** 7. Categorizing books based on their genres **L** 8. Recording the time it takes to complete a race **N** 9. Identifying the types of animals in a zoo **L** 10. Noting the sizes of shoes in a store **N** # Exercise B For each scenario or statement below, identify whether the data provided is nominal (N), ordinal (O), discrete (D), or continuous (C). 1. The blood types of students in the class (A, B, AB, O) **N** 2. The finishing positions of athletes in a race (1st, 2nd, 3rd) **O** 3. The number of books borrowed from the library last month **D** 4. The heights of students measured in centimeters **C** 5. The brands of smartphones used by students **N** 6. The ratings of a movie (1 star, 2 stars, 3 stars, etc.) **O** 7. The number of female students in the classroom **D** 8. The distance(km) students travel from home to school **C** 9. The types of weather observed during a week **N** 10. The time it takes for students to complete a math test **C** # Methods of Data Collection - **Surveys and Questionnaires:** - Description: Surveys involve asking individuals a set of predetermined questions, often in written form, to gather information about their opinions, behaviors, or characteristics. - Application: Used in social sciences, market research, and public opinion polls. - Advantages: Cost-effective, can reach a large audience, standardized format. - Challenges: Response bias, limited depth of information. - Examples: - Effects of modular distance learning and online learning. - Causes of cigarette smoking at young age. - **Interviews:** - Description: Interviews involve direct interaction between a researcher and a participant, where questions are asked and responses are recorded. - Application: Common in qualitative research, case studies, and in-depth investigations. - Advantages: Allows for in-depth exploration, flexibility in questioning, and clarification of responses. - Challenges: Time-consuming, potential for interviewer bias. - Examples: - Point of view of parents about cancellation of classes during typhoons. - Survey about the gate price of coconut product between buyers. - **Observations:** - Examples: - The increasing numbers of customers entering a coffee shop. - Attitude of Grade 7 students inside the classroom. - **Experiments:** - Description: Researchers manipulate variables to observe the effect on the outcome. Controlled conditions help establish cause-and-effect relationships. - Application: Common in natural sciences, psychology, and medicine. - Advantages: Allows for causal inference; high internal validity. - Challenges: Artificial settings may limit generalizability, ethical concerns. - **Case Studies:** - Description: In-depth examination of a single case or a small number of cases to gain insights into complex phenomena. - Application: Common in psychology, medicine, and social sciences. - Advantages: Rich, detailed information; suitable for complex or unique cases. - Challenges: Limited generalizability, potential for researcher bias. # Sampling Techniques - **Sampling:** - Is the process of selecting a subset of individuals or elements from a larger population for study. - **Sample:** - Is a subset of the population under study. - **Population:** - Is the set of all possible cases from which data are collected. - **Simple Random Sampling:** - Every individual in the population has an equal chance of being selected. - Example - Conducting a Classroom Survey: 1. **Identify the Population:** The population is all the students in the school, totaling 500. 2. **Assign a Number to Each Individual:** Assign a unique number to each student in the school. For example: - 1. Emma - 2. Roldan - 3. Michael - 4. Venus - 500. Tonny 3. **Determine the Sample Size:** Decide on the sample size you want for your survey. Let's say you want a sample size of 50 students. 4. **Use a Random Selection Method:** Randomly select the sample. You can use various methods. One simple way is to use a random number generator or draw numbers from a hat. Examples of random numbers can be 27, 142, 305, 48, 219, 498. 5. **Select the Chosen Individuals:** Identify the students corresponding to the randomly generated numbers. 6. **Invite the Selected Individuals to Participate:** Reach out to the selected students and invite them to participate in your survey on the effectiveness of reviewing early in the morning. - Population = 500 - Sample = 50 - 1. Emma - 2. Roldan - 3. Michael - 4. Venus - ... - 500. Mark - 34 - Montar - 25 - Sabina - 250 - Susan - 16 - Tonny - 375 - Mackoy - 3 - Michael - **Stratified Sampling:** - Dividing the population into subgroups (strata) and then randomly sampling from each subgroup. - Example - assessing Academic Performance in a School: 1. **Identify the Population:** The population, in this case, is all the students in the junior high school, totaling 600. 2. **Define Strata:** Divide the population into strata based on the characteristics of interest. In this example, the strata are the different grade levels: Grade 7, Grade 8, Grade 9, and Grade 10. 3. **Determine the Sample Size:** Decide on the overall sample size you want and the proportion of the sample from each stratum. Let's say you want a total sample size of 100 students, with the goal of representing each grade level proportionally. Sample size allocation: - Grade 7: 25 students - Grade 8: 25 students - Grade 9: 25 students - Grade 10: 25 students 4. **Randomly Select Within Strata:** Use random sampling within each stratum to select the specified number of students. You can use methods like random sampling technique. For example, if you are using a random number generator, generate 25 random numbers for each grade level. - Population: 600 students - Sample: 100 students - Grade 8 - 25 students - Grade 7 - 25 students - Grade 9 - 25 students - Grade 10 - 25 students - **Systematic Sampling:** - Selecting every nth individual from the population after a random start. - Example - Surveying Customers in a coffee shop: 1. **Identify the Population:** The population is all the customers present in a coffee shop during a specified time, totaling 500 individuals. 2. **Determine the Sample Size:** Decide on the overall sample size you want. Let's say you want to survey 50 customers. 3. **Random Start:** Choose a random starting point within the first k individuals. For example, randomly select the 2nd customer as your starting point. - total population - $K = \frac{500}{50} = 10$ 4. **Select the Chosen Individuals:** Survey every 10th customer from the randomly chosen starting point until you reach the desired sample size. Starting from the 2nd customer, survey the 12th, 22nd, 32nd, and so on until you've surveyed 50 customers. - 2. Emma - 12. Roldan - 22. Michael - 32. Venus - 492. Tonny # Methods of Data Collection (Activity) Direction: Identify the appropriate method of collecting data for each statement. 1. Point of view of parents about the matatag curriculum. **Interview** 2. Effects of modular distance learning and online learning. **Survey/Questionnaire** 3. Germination rates of monggo seeds. **Experiment** 4. The impact of playing online games to the grade 7 students. **Experiment** 5. The increasing numbers of students with no GMRC. **Observation** # Sampling Techniques (Activity) Direction: For each scenario provided, choose the appropriate sampling technique to be employed. - **Scenario 1:** You are conducting a survey to understand the preferences of students in a large university. To ensure representation from each academic department, you decide to sample 20 students from each department. **Stratified Sampling** - **Scenario 2:** You are conducting research on the preferences of customers in a specific shopping mall regarding product placement. **Systematic Sampling** - **Scenario 3:** You want to investigate the average commuting time of employees in a large office building with multiple departments. **Simple Random Sampling** - **Scenario 4:** You are interested in understanding the factors contributing to the success of students in a particular school, considering both academic performance and extracurricular achievements. **Stratified Sampling** - **Scenario 5:** In a city park, you want to survey visitors to gather feedback on park facilities. To make the survey process efficient, you decide to survey every 8th visitor who enters the park. **Systematic Sampling** # Frequency Distribution Table - Is a systematic way of presenting data using a table. - The data are grouped into different intervals or numbers of classes assigned by the researcher. Usually, the ideal number of classes is from 5 to 20 only. | Favorite Filipino Snacks | Tally | Frequency | |---|---|---| | banana cue | || 2 | | chicharon | ||| 3 | | lugaw | | 1 | | lumpia | ||| 4 | | puto | || 2 | | taho | || 2 | | turon | | 1 | ## Frequency Distribution Table (FDT) - A frequency distribution table (FDT) is a way to organize data by grouping it into categories or intervals and showing the number of times each occurs. # Graphs For Kids - A graphic representation of data using a picture. # Grade 7 Graphical Representation of Data (Part 1) - Pie and Bar Graphs ## Objectives - Use appropriate graphs to represent organized data: pie graph & bar graph - Interpret statistical graphs ## Review - **Frequency Distribution Table (FDT)** | Favorite Filipino Snacks | Frequency | |---|---| | Chicharon | 3 | | Taho | 4 | | Banana Cue | 7 | | Puto | 1 | | Age Range | Frequency | |---|---| | 17-18 | 21 | | 15-16 | 37 | | 13-14 | 40 | | 10-12 | 32 | ## Review - **Extended Type of FDT** | Favorite Filipino Snacks | Frequency | Relative Frequency | Percentage | |---|---|---|---| | Chicharon | 3 | 3/15 = 0.20 | 20% | | Taho | 4 | 4/15 = 0.27 | 27% | | Banana Cue | 7 | 7/15 = 0.47 | 47% | | Puto | 1 | 1/15 = 0.06 | 6% | Total Frequency = 15 **Relative Frequency = Frequency / Total Frequency** - **Relative Frequency:** Helps in understanding the proportion of each category compared to the whole. # Pie Graph - A pie graph (or chart) is a circular chart divided into slices, where each slice represents a proportion or percentage of the total. - **Often used for categorical data** - **Most effective for fewer data types or categories** - **Used to emphasize how a part contributes to the total** ## Constructing a Pie Graph **Example:** Favorite Filipino Snacks Survey in a Class of 15 Students | Favorite Filipino Snacks | Frequency | Relative Frequency | Percentage | Angle of the Sector | |---|---|---|---|---| | Chicharon | 3 | 0.20 | 20% | 0.2 x 360° = 72° | | Taho | 4 | 0.27 | 27% | 0.27 x 360°= 97.2° | | Banana Cue | 7 | 0.47 | 47% | 0.47 x 360°=169.2° | | Puto | 1 | 0.06 | 6% | 0.06 x 360°= 21.6° | Pie Chart: - Puto = 6% - Chicharon = 20% - Taho = 27% - Banana Cue = 47% **Steps:** 1. Determine the central angles of each slices (sector). 2. Draw the pie graph with the slices. 3. Label and color the slices. ## Interpreting a Pie Graph **Example:** Monthly Expenses of a Household - Pie Chart: - Others - 15% - Transportation - 15% - Utilities - 20% - Food - 50% **Questions:** 1. What is the largest expense for the household? **Food** 2. If the total monthly income is P20,000, how much is spent on Utilities? **($$\frac{20}{100}$$ x $20,000 = $P4,000)** 3. What percentage of the income is spent on Transportation and Others combined? **30%** 4. If the family wants to reduce spending on Food to 40%, how much money would be saved? # Bar Graph - A bar graph uses rectangular bars to represent data. The height or length of the bar corresponds to the data value, making it easy to compare categories. - **Works best for discrete categories (e.g., months, products, survey responses)** - **Clear comparison between different data sets** ## Constructing a Bar Graph **Example:** Amount of time a student spent on various app activities. | App Activity | Screen Time (Hours) | |---|---| | Social Media | 3.5 | | Streaming | 2 | | Games | 1.5 | | Education | 2.5 | | Messaging | 1 | **Bar Graph:** - **Daily Screen Time Usage by App** - y-axis: Screen Time (Hours) - x-axis: App Activity - Values: - Social Media = 3.5 Hours - Streaming = 2 hours - Games = 1.5 hours - Education = 2.5 hours - Messaging = 1 hour **Steps:** 1. Set up the axes. 2. Add the titles and labels. 3. Determine the scale and range of the numerical axis. 4. Draw the bars. ## Interpreting a Bar Graph **Example:** Popular Food Items Sold at a Food Stall - **Bar Graph:** - x-axis: Food Item - y-axis: Units Sold - Values: - Fried Chicken = 48 units - Burgers = 30 units - Spaghetti = 30 units - Lumpia = 35 units - Halo-Halo = 25 units **Questions:** 1. Which food item was sold the most? **Fried Chicken** 2. What is the total number of food items sold? **168 units** 3. If the food stall wants to increase sales of Halo-Halo, what strategies might they use based on the data? # Activity Read each situation below and choose the graph type that best represents the data. Justify your choice. 1. A toy store wants to compare the number of toy cars, dolls, puzzles, and board games sold last week. **Bar Graph - Shows comparison of the number of toys sold.** 2. A school cafeteria tracks the percentage of students who prefer different lunch options: rice meals, sandwiches, pasta, and salads. **Pie Graph - Shows the proportion of students who prefer each lunch option.** 3. A monthly report shows how a family spends their income across different categories: food, rent, utilities, and savings. **Pie Graph - Shows the proportion of income spent on each category.** 4. A retailer analyzes the sales of different shoe brands in their store during a one-month period to see which brand sold the most. **Bar Graph - Shows the comparison of sales of each shoe brand.** # Answers 1. **Bar Graph:** Effective for comparing toy sales by category. 2. **Pie Graph:** Best for showing proportions of student preferences for lunch. 3. **Pie Graph:** Suitable for showing how income is distributed across categories as percentages. 4. **Bar Graph:** Best for comparing sales performance of shoe brands.