Frequency Distributions and Visualizing Data

Histograms, Boxplots and Ogives

 Learning Objectives

Create and interpret Histograms, Boxplots and Ogives

Histograms:

  • A type of ‘bar chart’ organized by classes/categories created for the data (bins)
  • Where the heights of the bars equal to the frequencies of those classes
  • Useful for determining the ‘shape’ of the distribution of the data

Box Plots:

  • The ‘box’ spans from quarter 1 to quarter 3
  • The middle line of the box indicates the median
  • If there are outliers (extremely large/small values), they are indicated by dots or asterisks (*)
  • The lower and upper lines (fences) indicate the highest and lowest non-outlier values in the data
  • Is a great visual tool to help understand the dispersion/spread of the data

Ogives:

  • A line chart where the heights are the cumulative frequency values
  • Useful for estimating the percent of data that lie below or above particular variables or values[1]
  • Can be made by inserting in a line chart where the y-axis values are the cumulative percent frequencies and the x-axis is the class limits column from the cumulative frequency table
  • Useful for determining the ‘spread’ of the data

Creating a Histogram in Excel (video)

Example 12.1.1

Problem Setup: Again, we are working with the 30 students’ heights from BCIT (click here to download as Excel sheet) and see the table of values below.

173 153 172 191 173 167 156 169 175 169
159 163 177 155 152 178 172 188 152 171
174 183 192 151 159 184 170 186 155 156

Question: Can you create a histogram of these heights?

Solution: Click here to view the Excel solutions shown in the above video.

Creating a BOXPLOT in Excel (video)

Example 12.1.2

Problem Setup: Again, we are working with the 30 students’ heights from BCIT (click here to download as Excel sheet) and see the table of values below.

173 153 172 191 173 167 156 169 175 169
159 163 177 155 152 178 172 188 152 171
174 183 192 151 159 184 170 186 155 156

Question: Can you create a boxplot of these heights?

Solution: Click here to view the Excel solutions shown in the above video.

Understanding Outliers in Boxplots and Histograms (video)

Example 12.2.1

Problem Setup: We will now revisit the student survey data inputted by students in 2019 (Click here to download).

Question: Can you create an explain the values in the boxplot created for the students’ heights?

Solution: Click here to view the Excel solutions shown in the above video.

Creating Ogives in Excel (video)

Example 12.1.3

Problem Setup: Again, we are working with the 30 students’ heights from BCIT (click here to download as Excel sheet).

173 153 172 191 173 167 156 169 175 169
159 163 177 155 152 178 172 188 152 171
174 183 192 151 159 184 170 186 155 156

Question: Can you create an ogive of these heights?

Solution: Click here to view the Excel solutions shown in the above video.

Key Takeaways (EXERCISE)

Key Takeaways: Histograms, Boxplots and Ogives

Your Own Notes (EXERCISE)

  • Are there any notes you want to take from this section? Is there anything you’d like to copy and paste below?
  • These notes are for you only (they will not be stored anywhere)
  • Make sure to download them at the end to use as a reference

  1. https://byjus.com/maths/ogive/#:~:text=The%20word%20Ogive%20is%20a,calculated%20using%20a%20frequency%20table.

License

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An Introduction to Business Statistics for Analytics (1st Edition) Copyright © 2024 by Amy Goldlist; Charles Chan; Leslie Major; Michael Johnson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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