Frequency & Data

Class Information and Updates

  • Class Format:

    • Temporary decision on class format due to weather poses uncertainty; notification will be sent via email on Sunday regarding whether the upcoming Monday class will be online.

  • Textbook Availability:

    • Hard copies of the course textbook are available at the library.

    • The textbook is reserved, allowing a maximum borrowing period of two days.

    • Students are encouraged to make copies of essential pages rather than the entire book.

    • An electronic version of the textbook can also be purchased online or rented through services like Cost Smart for the semester.

  • Booster Workshop:

    • The department offers a free, fully online - MAS 111 Booster Workshop.

    • This workshop includes:

    • Access to lessons and materials via Brightspace.

    • Optional weekly lab sessions (Tuesday 9-10 AM, and Friday 10-11 AM) with an instructor.

    • Participation may yield bonus credits for students attending multiple sessions.

    • Registration details include sending students’ emails, names, sections, and CUNY IDs to a provided email address.

Class Structure and Levels of Measurement

  • Measurements:

    • Previous class discussions include the levels of measurement:

    • Nominal Level: Only qualitative data; categories are unordered.

    • Ordinal Level: Can apply to qualitative and quantitative data; categories can be ordered.

    • Interval Level:

      • Must be quantitative.

      • Differences between data entries are meaningful, allowing for mathematical operations (e.g., subtraction).

      • Example applications include time and temperature measurements.

      • Notably, a zero at this level does not imply a total absence of quantity (e.g., 0°C does not mean no temperature).

    • Ratio Level:

      • Extends the interval level with an inherent zero representing a total absence of the quantity (e.g., 0 grams means no mass).

      • Ratios can be calculated; numerical values can be compared and expressed as multiples.

Practical Examples of Levels of Measurement

  • Interval Level Example:

    • Measuring temperatures where valid differences can be calculated but not ratios (e.g., comparing temperatures of 20°C and 40°C).

  • Ratio Level Example:

    • Comparing the length of 10 inches to 5 inches (10 inches is 2 times longer than 5 inches).

  • Practical Application:

    • Data representations in classes of statistics, for example, in sports statistics (baseball wins) analyze and illustrate data through classes and frequency tables.

Frequency Distributions and Graphs

  • Defining Frequency Distribution:

    • A frequency distribution is a table that summarizes data points into classes or intervals, presenting the count (frequency) of entries per class.

    • Frequency distribution includes two main columns:

    • Class/Interval: Shows the ranges of data.

    • Frequency (f): Shows the number of data points within each class.

  • Constructing Frequency Distribution:

    • Steps involved include:

    1. Deciding the Number of Classes: Typically between 5-20.

    2. Finding Class Width: Determine the range (maximum - minimum) divided by the number of classes; round up as necessary.

    3. Establishing Class Limits: Use minimum data entry for the first class limit, and add class width for subsequent classes.

    4. Calculating Frequencies: Create tally marks for data entries in the appropriate class and count to obtain frequency values.

    5. Verifying Total Frequencies: Ensure the total frequency matches the number of entries in the dataset.

  • Additional Concepts:

    • Cumulative Frequency: The running total of frequencies as you advance through the classes, increasing with each new data class.

    • Midpoint Calculation: The average of the lower and upper limits for each class.

    • Relative Frequency: The fraction of the total represented by each class's frequency (frequency/class total).

  • Graphing Frequency Distributions:

    • Histogram requirements include ensuring that bars touch and represent frequency classes accurately. Class boundaries may be utilized to attain this, by adjusting class limits.