Overview
This lecture covered how to interpret histograms, focusing on identifying variables and objects of interest, reading frequencies, and calculating percentages from histogram data.
Identifying Objects of Interest and Variables
- The object of interest refers to the population or group being studied (here: statistics students).
- The variable is the measured characteristic (here: number of miles driven to school each day).
- The vertical axis (frequency) represents the count of objects (students).
- The horizontal axis represents the variable (miles driven).
Reading Histogram Frequencies
- To answer "How many students?" identify the frequency (height) of the relevant histogram rectangle (bin).
- For example, 17 students commute between 10 to 15 miles to school each day (from the relevant bin's height).
- To find students commuting over 50 miles, add the frequencies of the last two bins (result: 2 students).
Calculating Percentages from Histogram Data
- To find the percent of students in a group, create a fraction: (number in group) ÷ (total number of students).
- For students commuting less than five miles, use the first bar's frequency: 7 students.
- The total number of students (n) is 67.
- Percent = (7 ÷ 67) × 100 = 10.4%.
Key Terms & Definitions
- Histogram — a bar graph showing the distribution of a variable's frequency.
- Object of Interest — the group or population being analyzed.
- Variable — the characteristic measured (e.g., miles commuted).
- Frequency — the number of objects falling within a specific bin/range.
- Bin — the interval or range of values displayed as individual bars in a histogram.
- n — symbol representing total sample size.
Action Items / Next Steps
- Practice identifying variables and objects of interest in other histogram examples.
- Calculate more frequencies and percentages using similar histogram data.