Histogram Examples in Descriptive Statistics

Explore diverse examples of histograms in descriptive statistics, showcasing practical applications across various contexts.
By Jamie

Understanding Histograms in Descriptive Statistics

Histograms are a crucial tool in descriptive statistics, allowing us to visualize the distribution of a dataset. By representing data in a graphical format, histograms help identify patterns, trends, and anomalies. Below are three diverse examples that illustrate the use of histograms in different contexts.

Example 1: Student Test Scores Distribution

In an educational setting, understanding the distribution of student test scores can provide valuable insights into overall performance and areas needing improvement. A teacher may collect scores from a math exam taken by 30 students:

  • Scores: 56, 67, 78, 45, 88, 72, 65, 90, 82, 54, 62, 75, 83, 91, 69, 77, 70, 80, 86, 59, 64, 68, 81, 73, 87, 92, 60, 74, 78, 85

To analyze this data, the teacher creates a histogram with score intervals (bins) of 10:

  • 0-10: 0
  • 10-20: 0
  • 20-30: 0
  • 30-40: 0
  • 40-50: 1
  • 50-60: 4
  • 60-70: 6
  • 70-80: 7
  • 80-90: 7
  • 90-100: 5

This histogram reveals that most students scored between 70-80 and 80-90, indicating a solid understanding of the material. The teacher can use this information to address areas where students struggled.

Notes:

  • Variation: Changing bin sizes could provide different insights. A narrower bin width might reveal more details about performance distribution.

Example 2: Daily Temperatures in a City

Meteorologists often analyze temperature data to identify trends and patterns in climate. Consider a dataset representing daily high temperatures (in degrees Fahrenheit) recorded over a month in a city:

  • Temperatures: 75, 78, 72, 81, 85, 80, 77, 79, 74, 83, 88, 90, 92, 78, 76, 81, 84, 89, 91, 93, 76, 75, 82, 80, 78, 77, 81, 85, 88, 86

A histogram can be constructed with temperature bins of 5 degrees:

  • 70-75: 5
  • 75-80: 8
  • 80-85: 7
  • 85-90: 6
  • 90-95: 4

The histogram indicates that the majority of daily highs were clustered around the 75-80 and 80-85 ranges, with fewer days experiencing temperatures above 90. This information can help in predicting future weather patterns.

Notes:

  • Variation: Comparing histograms from different months can highlight seasonal changes in temperature.

Example 3: Customer Purchase Amounts in a Retail Store

Retail analysts frequently use histograms to evaluate customer spending behavior. Suppose a retail store records the following purchase amounts (in dollars) from 50 customers:

  • Purchase Amounts: 20, 25, 30, 45, 50, 55, 25, 35, 40, 60, 70, 80, 90, 15, 100, 120, 80, 45, 50, 55, 60, 30, 25, 40, 35, 55, 70, 80, 90, 15, 20, 30, 45, 50, 60, 75, 85, 90, 95, 100, 110, 120, 130, 140, 150, 80, 60, 50, 40, 30

To visualize this data, the store can create a histogram with purchase bins of $20:

  • 0-20: 5
  • 20-40: 15
  • 40-60: 12
  • 60-80: 10
  • 80-100: 5
  • 100-120: 3
  • 120-140: 1
  • 140-160: 1

This histogram shows a peak in the $20-40 range, indicating that many customers are making smaller purchases. The store can use this data to tailor marketing strategies or promotions.

Notes:

  • Variation: Analyzing customer purchases over time can reveal trends in spending behavior, helping retailers adjust inventory and pricing strategies.