Measures of Position

Chapter 2Section 5NotesCoach Bridges

Fractiles Numbers that partition, or divide, an

ordered data set into equal parts The median is a fractile because it

divides an ordered data set into two equal parts

Quartiles There are three quartiles These quartiles approximately divide an

ordered data set into four equal parts One quarter of the data falls on or below the

first quartile Q1 One half the data falls on or below the second

quartile Q2 About three quarters of the data falls on or

below the third quartile Q3

5 Number Summary

1. Minimum2. Maximum3. Quartile 14. Quartile 2 – Median5. Quartile 3

Examples Find the 3 quartiles of the following

data set

13, 9, 18, 15, 14, 21, 7, 10, 11, 20, 5, 18, 37, 16, 17

2nd Example Find the 3 quartiles of the following

data set

23, 25, 30, 23, 20, 22, 21, 15, 25, 24, 30, 25, 30, 20, 23, 29, 20, 19, 22, 23, 29, 23, 28, 22, 28

Box and Whisker Plot Find the five-number summary Construct a horizontal scale that

spans the range of the data Plot the five number summary Draw a box from Q1 to Q3 and

vertical line through Q2 Draw Whiskers for min and max

Interquartile Range (IQR) Difference between the first and the

third quartile in a data set IQR = Q3 – Q1

Standard Score – Z Score

Z = value – mean standard deviation