Lecture 1

Welcome & Relative Frequency Histograms

Published

August 29, 2023

1.4 Relative Frequency Histograms

Table 1: Birthweights of 30 Full-Term Newborn Babies
7.2 7.8 6.8 6.2 8.2
8.0 8.2 5.6 8.6 7.1
8.2 7.7 7.5 7.2 7.7
5.8 6.8 6.8 8.5 7.5
6.1 7.9 9.4 9.0 7.8
8.5 9.0 7.7 6.7 7.7
  • Definitions
    • class
    • class boundaries
    • class width
    • class frequency
    • relative frequency histogram

Choosing Number of Classes

Table 2: Choosing the number of classes
25 50 100 200 500
6 7 8 9 10

Choosing class width

Range of Data

\[ 9.4 - 5.6 = 3.8 \\ \]

Divide and round

\[ 3.8/8 = .475 \approx .5 \]

Class Boundaries
[5.6,6.1)
[6.1,6.6)
[6.6,7.1)
[7.1,7.6)
[7.6,8.1)
[8.1,8.6)
[8.6,9.1)
[9.1,9.6)
  • Method of left inclusion

Tally Data in each of Boundaries

Class.Boundaries Freq Relative.Frequency
[5.6,6.1) 2 2/30
[6.1,6.6) 2 2/30
[6.6,7.1) 4 4/30
[7.1,7.6) 5 5/30
[7.6,8.1) 8 8/30
[8.1,8.6) 5 5/30
[8.6,9.1) 3 3/30
[9.1,9.6) 1 1/30

Draw Histogram

Examples with different number of classes (or bins)

The graphs below show what happens if you use 3 and 20 classes - compare to the figure above

3 classes - you lose information on the tails

20 classes - lots of between items - harder to get a general sense of shape

Example 1.11

Table 3: Number of Visits in Typical Week for 25 Customers
6 7 1 5 6
4 6 4 6 8
6 5 6 3 4
5 5 5 7 6
3 5 7 5 5
  • Use intgers as class definitions
Class.Boundaries Freq Relative.Frequency
[0.5,1.5) 1 0.04
[1.5,2.5) 0 0.00
[2.5,3.5) 2 0.08
[3.5,4.5) 3 0.12
[4.5,5.5) 8 0.32
[5.5,6.5) 7 0.28
[6.5,7.5) 3 0.12
[7.5,8.5) 1 0.04

Using Histograms

  • data location
  • data shape (skewed left, skewed right)
  • proportion/probability

Making histograms in Excel

Download a sample Excel file here

Looking forward

  • sample vs population
  • if you look at 30 more birth weights will you have same histogram?

Other Resources

Homework

1.4.17-20, 1.4.21-22, 1.4.26, 1.4.33

Answers: Chapter 1 - Section 1.4