Measures of Position

Section 2.5

StatisticsMrs. SpitzFall 2008

Larson/Farber Ch 2

Objectives/Assignment

§ How to find the first, second and third quartiles of a data set.

§ How to find the interquartile range of a data set§ How to represent a data set graphically using a

box-and-whisker plot§ How to interpret other fractiles such as percentsAssignment: pp78-82 #1-32 all – Due WednesdayChapter 2 Review pp. 97-100 #1-45 all Due FridayChapter 2 Test – Friday – Binder Check with notes

due FRIDAY.

Larson/Farber Ch 2

Definitions

§ Fractiles are numbers that partition or divide an ordered data set into equal parts. For instance, the median is a fractile because it divides an ordered data set into two equal parts.

§ The thre quartiles Q1, Q2 and Q3 approximately divide an ordered data set into four equal parts. About one quarter of the data falls on or below the first quartiles, Q1. About one half of the data alls on or below the second quartile Q2, and about three quarters of the data falls on or below the third quartile Q3. The second quartile is the same as the median of the data set.

Larson/Farber Ch 2

Definitions

§ The interquartile range (IQR) of a data set is the difference between the first and third quartiles.

Interquartile range (IQR)= Q3 – Q1

Larson/Farber Ch 2

You are managing a store. The average sale for each of 27 randomly selected days in the last year is given. Find Q1, Q2, and Q3.

28 43 48 51 43 30 55 44 48 33 45 37 37 42 27 47 42 23 46 39 20 45 38 19 17 35 45

3 quartiles Q1, Q2 and Q3 divide the data into 4 equal parts. Q2 is the same as the median. Q1 is the median of the data below Q2.

Q3 is the median of the data above Q2.

Quartiles

Larson/Farber Ch 2

The data in ranked order (n = 27) are:17 19 20 23 27 28 30 33 35 37 37 38 39 42 42 43 43 44 45 45 45 46 47 48 48 51 55.

Median rank (27 + 1)/2 = 14. The median = Q2 = 42.

There are 13 values below the median. Q1 rank= 7. Q1 is 30. Q3 is rank 7 counting from the last value. Q3 is 45.

The Interquartile Range is Q3 – Q1 = 45 – 30 = 15.

Finding Quartiles

Larson/Farber Ch 2

Box and Whisker Plot

5545352515

A box and whisker plot uses 5 key values to describe a set of data. Q1, Q2 and Q3, the minimum value and the maximum value. Q1

Q2 = the medianQ3

Minimum valueMaximum value

30 42451755

42 453017 55

Interquartile Range = 45 – 30 = 15

Larson/Farber Ch 2

Percentiles

Percentiles divide the data into 100 parts. There are 99 percentiles: P1, P2, P3…P99.

A 63rd percentile score indicates that score is greater than or equal to 63% of the scores and less than or equal to 37% of the scores.

P50 = Q2 = the median

P25 = Q1 P75 = Q3

Larson/Farber Ch 2

Percentiles

114.5 falls on or above 25 of the 30 values. 25/30 = 83.33.

So you can approximate 114 = P83.

Cumulative distributions can be used to find percentiles.