12.1 Data Collection, Organization, and Representation
Data Collection Methods
Data can be collected using various statistical methods depending on the situation:
- Interview: Direct questioning to obtain information from individuals.
- Questionnaire / Survey: Using a set of written questions given to respondents.
- Observation: Recording observed events or behavioral data directly.
- Experiment: Conducting tests under controlled conditions to collect measurable numerical data.
Categorical vs Numerical Data
- Categorical Data: Qualitative data that classifies items into categories or labels (e.g., blood types, vehicle colors, favorite sports).
- Numerical Data: Quantitative data measured or counted as numerical values:
- Discrete Data: Countable values as whole numbers (e.g., number of siblings, goal count).
- Continuous Data: Measurable values on a continuous scale (e.g., height, mass, time).
Data Representation Methods
- Bar Chart: Uses rectangular bars of uniform width where the height/length corresponds to frequency. Suitable for categorical or discrete numerical data.
- Pie Chart: A circular chart divided into sectors where each sector angle is proportional to the category frequency:
$$\text{Sector Angle} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 360^\circ$$
- Line Graph: Uses connected points to display changes in data over a continuous period of time.
- Stem-and-Leaf Plot: Organizes raw numerical data by splitting each value into a 'stem' (leading digits) and a 'leaf' (trailing digit), preserving original data values.
- Dot Plot: Displays individual data points as dots above a horizontal number line to show distribution and clustering.
12.2 Interpretation of Data Representations
- Mode / Highest Frequency: Identified by the tallest bar in a bar chart, largest sector in a pie chart, or line peak in a dot plot.
- Trends & Patterns: Line graphs show increasing, decreasing, or stable trends over time.
- Data Skewness and Range: Dot plots and stem-and-leaf plots show data spread, minimum/maximum values, and extreme values (outliers).