Slide 1: Title Slide

[Virtual Presenter] Slide 1: Title Slide Title: Frequency Tables: Organizing and Summarizing Data Subtitle: An Essential Tool in Statistics Visual: A simple, eye catching graphic showing disorganized numbers being sorted into a neat table..

[Audio] Slide 2: What is a Frequency Table Slide 2: What is a Frequency Table? Definition: A table that lists categories or values and shows the number of times (or frequency) each one occurs in a data set. Key Purpose: To take raw data (a jumbled list of numbers) and make it easily understandable. To quickly identify the most common (mode) and least common values. To serve as the foundation for creating visual graphs (like histograms and bar charts). Visual: An image comparing a list of 20 raw numbers to a simple 2-column frequency table Definition: A table that lists categories or values and shows the number of times (or frequency) each one occurs in a data set. Key Purpose: To take raw data (a jumbled list of numbers) and make it easily understandable. To quickly identify the most common (mode) and least common values. To serve as the foundation for creating visual graphs (like histograms and bar charts). Visual: An image comparing a list of 20 raw numbers to a simple 2-column frequency table.

[Audio] Slide 3: Two Main Types of Frequency Tables The type of table you use depends on the nature of your data. Type Best Used For Data Type Example Ungrouped Small data sets or when data has few unique values. Discrete (countable values, like shoe size or number of pets) Scores on a 10-point quiz. Grouped Large data sets or when data is continuous and has many different values. Continuous (measurable values, like height, weight, or time) Weights of 100 packages. Visual: Side by side examples of a small ungrouped table and a grouped table with class intervals..

[Audio] 🔢 Ungrouped Frequency Tables Slide 4: Building an Ungrouped Table (Steps) Data Set Example: Scores on a quiz: 5, 8, 7, 5, 9, 7, 7, 6, 8, 5 Step 1: List the Values/Categories List all unique data values (Scores) in the first column, usually in ascending order: 5, 6, 7, 8, 9. Step 2: Tally the Data Go through the raw data and make a tally mark ($\text$) next to the corresponding score. Use a gate ($\text$) for the fifth mark. Step 3: Count the Frequency (f) Convert the tally marks into a number (Frequency) in the final column. Visual: A simple 3-column table showing the progression: Value | Tally | Frequency..

[Audio] Slide 5: Adding Relative and Cumulative Frequency Frequency tables can be extended to include more information. Relative Frequency (R F ): The proportion of the total that falls into a specific value/category. Formula: $\text = \frac}}$ This is often expressed as a percentage: $\text \times 100\%$ Cumulative Frequency (C F ): The running total of the frequencies. It tells you how many data points are at or below a specific value. Visual: The completed table from Slide 4 with two extra columns for R F and C F.

[Audio] 📈 Grouped Frequency Tables Slide 6: The Need for Grouped Data Problem: If you have 50 different student ages, an ungrouped table would have 50 rows and be just as confusing as the raw data! Solution: We use Class Intervals (or bins) to group the data into manageable ranges. Rule of Thumb: Use between 5 and 20 classes. They must be mutually exclusive (non overlapping). Visual: A large list of raw numbers that demonstrates why grouping is necessary..

[Audio] Slide 7: Constructing Class Intervals Steps to Build Intervals: 1. Find the Range (R): Highest Value Lowest Value. 2. Choose the Number of Classes ($k$): Let's say $k=5$. 3. Calculate Class Width ($i$): $i \approx \frac}$. Always round up to a convenient number. 4. Set the Limits: Start the first interval with the lowest value and add the class width to define the intervals (for example, 10-19, 20-29, 30-39, et cetera). Key Terms: Lower Class Limit (smallest value in the interval) and Upper Class Limit (largest value in the interval). Visual: A graphic illustrating the calculation of the range and class width..

[Audio] Slide 8: Completed Grouped Table Example Class Interval (Scores) Tally Frequency (f) 50 – 59 $\text$ 2 60 – 69 $\text$ 4 70 – 79 $\text\hspace\text$ 8 80 – 89 $\text\hspace\text$ 10 90 – 99 $\text\hspace\text$ 6 Total 30 Talking Point: The Modal Class is the interval with the highest frequency (80-89 in this case). Visual: A clearly presented grouped frequency table..

[Audio] Slide 9: Visualization (The Power of the Table) Frequency tables are the starting point for visual data analysis. Histogram: Used for Grouped Data. Bars must touch because the data is continuous. The height of the bar is the frequency. Bar Chart: Used for Ungrouped Data (or categorical data). Bars are usually separated. Visual: A side by side comparison of a Histogram (for grouped data) and a Bar Chart (for categorical data)..

[Audio] Slide 10: Conclusion and Q&A Summary: Frequency tables are fundamental in statistics for transforming raw data into meaningful summaries. They reveal the pattern and distribution of data. Application: Used everywhere from business reports to scientific research. (Q&A)--: Open the floor for questions. Visual: A final image showing a complete data analysis process flow..