5.1.2 Organizing Quantitative Data

Tables

Original Data

 2 2 2 4 5 3 3 3 3 2 1 2 3 5 3 4 3 1 2 3 5 3 2 1 3 2

Sometimes there are too many values to make a row for each one. In that case, we’ll need to group several values together.

 children frequency Relative frequency 1 3 3/26≈ 0.12 2 8 8/26≈ 0.31 3 10 10/26≈ 0.38 4 2 2/26≈ 0.08 5 3 3/26≈ 0.12

A discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of values, i.e., 0, 1, 2, 3, …

Original Data

 62 87 67 58 95 94 91 69 52 76 82 85 91 60 77 72 83 79 63 88 79 88 70 75 75

Histogram

 children frequency relative frequency 1 3 3/26≈ 0.12 2 8 8/26≈ 0.31 3 10 10/26≈ 0.38 4 2 2/26≈ 0.08 5 3 3/26≈ 0.12

Histogram

• height of rectangles is the frequency or relative frequency of the class
• widths of rectangles is the same and they touch each other

Frequency Polygon

 average commute frequency relative frequency 16–17.9 1 1/15≈ 0.07 18–19.9 2 2/15≈ 0.13 20–21.9 1 1/15≈ 0.07 22–23.9 6 6/15≈ 0.40 24–25.9 2 2/15≈ 0.13 26–27.9 1 1/15≈ 0.07 28–29.9 1 1/15≈ 0.07 30–31.9 1 1/15≈ 0.07

A frequency polygon

is drawn by plotting a point above each class midpoint and connecting the points with a straight line.

(Class midpoints are found by average successive lower class limits.)

Cumulative Tables and Ogives

 average commute frequency cumulative frequency 16–17.9 1 1 18–19.9 2 3 20–21.9 1 4 22–23.9 6 10 24–25.9 2 12 26–27.9 1 13 28–29.9 1 14 30–31.9 1 15

Cumulative tables

show the sum of values up to and including that particular category.

 average commute relative frequency cumulative relative frequency 16–17.9 1/15≈ 0.07 1/15≈ 0.07 18–19.9 2/15≈ 0.13 2/15≈ 0.20 20–21.9 1/15≈ 0.07 1/15≈ 0.27 22–23.9 6/15≈ 0.40 6/15≈ 0.67 24–25.9 2/15≈ 0.13 2/15≈ 0.80 26–27.9 1/15≈ 0.07 1/15≈ 0.87 28–29.9 1/15≈ 0.07 1/15≈ 0.94 30–31.9 1/15≈ 0.07 1/15≈ 1.00

An ogive is a graph that represents the cumulative frequency or cumulative relative frequency for the class.