graphing frequency

Histogram Definition and Purpose

  • Histogram: A type of bar graph that displays information about frequency.

    • Utilizes bar-style rectangles to indicate how often a data point falls into a specified category.

Types of Frequency in Histograms

  • Absolute Frequency Histogram:

    • The y-axis represents absolute frequency using numerical values.

  • Relative Frequency Histogram:

    • The y-axis represents relative frequency, expressed in percentage values.

Components of a Histogram

  • Axes Configuration:

    • Sometimes one or both axes feature an interval or range of numbers for scaling.

  • Parts of a Histogram:

    • Title: Describes the overall information of the graph.

    • Labels: Identifies what each axis represents.

    • Units Identification: Specifies the units used on each axis (e.g., minutes, days absent).

    • Grid Lines: Can be visible or invisible; serve to aid in reading the graph.

    • Scale:

    • Y-axis: Indicates either absolute or relative frequency.

    • X-axis: Represents frequency distribution of data.

    • Bars: Rectangular shapes indicating specific frequency values for the corresponding data range.

    • Source: Indicates the origin of the data presented in the graph.

Analyzing Graphs Before Answering Questions

  • Instruction: Before formulating answers regarding the histogram, it’s crucial to thoroughly analyze and comprehend the graph’s representation.

Examples of Histogram Analysis

Example 1: Average Travel Time to Work

  • Title: Average travel time to work in 68 major U.S. cities.

  • X-axis: Indicates the frequency distribution, measured in minutes spent commuting.

  • Y-axis: Represents absolute frequency.

  • First Bar Example:

    • Label: 15 to 19 minutes

    • Frequency: 13 cities (indicating 13 of the 68 cities in question have average commute times ranging from fifteen to nineteen minutes).

  • Questions for Analysis:

    • Most common commute time?

    • High frequency identified as 20 to 24 minutes (recognized as the answer).

    • Least common commute time?

    • Low frequency identified as 35 to 39 minutes (recognized as the answer).

Example 2: Attendance in Summer Enrichment Program

  • Title: Attendance in summer enrichment program.

  • X-axis: Represents the frequency distribution, measured in days absent.

  • Y-axis: Represents relative frequency in percentage terms.

  • First Bar Example:

    • Label: 0 days absent

    • Frequency: 29% (meaning 29% of students missed zero days).

  • Questions for Analysis:

    • What percentage missed only one day?

    • Estimated to be about 15%.

    • What percentage was absent for four or more days?

    • Breakdown of relevant data:

      • 4 days absent: 7%

      • 5 days absent: 5%

      • 6 days absent: 3%

      • 7 days absent: 5%

    • Total absent for 4 or more days:

    • Calculation: 7% + 5% + 3% + 5% = 20%.