Mathematics As A Tool: Data Management PDF

CHAPTER 4 MATHEMATICS AS A TOOL Lesson Discussion: Data Management Definition:  Statistics: involves the collection, summarization, presentation, and interpretation of data.  Data: is a set of values with respect to a cer...

CHAPTER 4 MATHEMATICS AS A TOOL Lesson Discussion: Data Management Definition:  Statistics: involves the collection, summarization, presentation, and interpretation of data.  Data: is a set of values with respect to a certain variable. Data is the backbone of any experiment.  Data Management: Explain that data management involves the systematic process of collecting, organizing, and analyzing data to derive meaningful insights.  Relevance: Highlight that in an era dominated by technology, data informs decisions in fields such as business, healthcare, education, and public policy. Variables and Types of Data Variables Definition: Variables are characteristics or properties that can vary or change within a dataset. Variables are categories we measure. For the case of numerical data, it can be age, time length, weight, etc. Types of Variables  Independent variables: Are see variables that stand alone and are not affected by other quantities we measure. Independent Variables are conventionally placed at the x-axis.  Dependent variable: The output variable in a function which depends on the value of the input or independent variable. Dependent Variables are conventionally placed at the y-axis. Types of Data  Qualitative Data: Non-numerical data that describes qualities or characteristics. Represent categories or groups. Example: Colors of cars (red, blue, green).  Quantitative Data: Represent numerical data that can be measured and compared (e.g., height, age, income). Example: In a survey about student preferences for study methods, responses might include qualitative data (like "group study") and quantitative data (like hours spent studying). Data Collection Methods  Surveys: Collecting data through questionnaires.  Experiments: Gathering data by manipulating variables in a controlled environment.  Observational Studies: Recording data based on observation without interference. Example: A school conducts a survey to assess students' study habits. The survey includes questions that yield both qualitative and quantitative data. Data Analysis Techniques  Types of Statistics : Descriptive and Inferential Statistics  o Descriptive Statistics: Is a branch of statistics that deals with collection, summarization, and presentation of data. It provides simple summaries and visualizations of data. This includes measures like averages, totals, and percentages, as well as charts and graphs. Summarizing data through measures such as mean, median, mode, and standard deviation. o Inferential Statistics: Is a branch of statistics that deals with the interpretation of data. Making predictions or inferences about a population based on a sample.  Data Visualization: Using graphs and charts to represent data visually. Example: After collecting survey data, students can calculate the average number of hours spent studying (mean) and create a bar chart to represent different study methods. Types of Data/Level of Measurement  Nominal Data: Data categorized without a natural order. Example: Types of fruit (apple, banana, cherry).  Ordinal Data: Data categorized with a natural order but no consistent difference between categories. Example: Rankings in a race (1st, 2nd, 3rd).  Interval Data: Numerical data with meaningful differences between values, but no true zero point. Example: Temperature in Celsius.  Ratio Data: Numerical data with meaningful differences and a true zero point. Example: Weight in kilograms.