"Constructing a frequency distribution and a histogram"

Shopping Times Analysis

Overview

• This document concerns the shopping times (in minutes) for 18 customers at a grocery store.
• The purpose is to create a grouped frequency distribution and a histogram of the data.

Data Summary

• Data Set: Shopping times (in minutes) recorded for 18 shoppers:
  • 21, 15, 30, 23, 17, 25, 37, 26, 35, 28, 27, 34, 38, 24, 18, 21, 31, 32

Part (a): Constructing a Grouped Frequency Distribution

• Class Width: Not specified; typically represented as a range (e.g., 5-, 10-minute intervals).

• Grouped Frequency Distribution Table:

  Class Interval	Frequency
  15 to 20	3
  21 to 26	6
  27 to 32	5
  33 to 38	4

Explanation of Grouped Frequencies:

• 15 to 20 minutes: 3 shoppers spent between 15 and 20 minutes.
• 21 to 26 minutes: 6 shoppers spent between 21 and 26 minutes.
• 27 to 32 minutes: 5 shoppers spent between 27 and 32 minutes.
• 33 to 38 minutes: 4 shoppers spent between 33 and 38 minutes.

Part (b): Constructing a Histogram

• Histogram Visualization:

  • A graphical representation of the frequency distribution with class intervals on the x-axis and frequency on the y-axis.

  • The height of the bars represents the number of shoppers in each class interval:

  • Steps to Create Histogram:

  • Label the x-axis with the class intervals (15-20, 21-26, etc.).

  • Label the y-axis with frequencies (0 to max frequency).

  • Draw bars for each class interval:

    • Bar for 15-20: Height = 3
    • Bar for 21-26: Height = 6
    • Bar for 27-32: Height = 5
    • Bar for 33-38: Height = 4

Final Note

• This exercise demonstrates how to summarize data distributions using frequency tables and histograms, crucial for statistical analysis and interpretation. Understanding these concepts helps analyze consumer behavior in a real-world context.