Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

3.4

Percentiles &

Box­and­Whisker Plots

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Measure of Position:~Used to describe the position a specific data value possesses in relation to the rest of the data~Quartiles and Percentile

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Percentile:

~For whole numbers P (1≤P≤99), the Pth percentile of a distribution is a value such that:

P% of the data fall at or below it

(100­P)% of the data fall at or above it

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Percentiles are commonly used in test results (SATs, etc.)

~If your score on an English achievement test was at the 89th percentile, what percentage of scores are at or below yours?

~If the scores ranged from 1 to 100 and your raw score is 95, does this mean that your score is at the 95th percentile?

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Quartiles:

~Percentiles that divide data into fourths

~First Quartile, Q1, is the 25th percentile

~Second Quartile, Q2, is the median (50th perc.)

~Third Quartile, Q3, is the 75th percentile

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Finding Quartiles:

1. Order data ­ smallest to largest

2. Find the median (Q2)

3. The first quartile, Q1, is the median of the lower half of the data; that is, it is the median of the data falling below the Q2 position (not including Q2)

4. The third quartile, Q3, is the median of the upper half of the data; that is, it is the median of the data falling above the Q2 position

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Interquartile Range = Q3 ­ Q1

~More resistant measure of spread

~If the mean and standard deviation are not a good representation of your data due to outliers, the median and interquartile range may be a better choice.

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Outliers:~The interquartile range provides a way for us to identify which data values are outliers

1.5 x IQR Rule for Outliers:

A data value is an outlier if it falls more than (1.5 x IQR) above Q3 or below Q1.

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Box­and­Whisker Plots:

~Uses the 5­number summary to create a plot

Minimum, Q1, Median, Q3, Maximum

(the minimum and maximum values are identified after any outliers are found)

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

Making a Box­and­Whisker Plot:

1. Set up a number line that will include all data

2. A central box is drawn from Q1 to Q3

3. A line in the box marks the median

4. Lines (whiskers) extend from the box out to the smallest and largest observations that are not outliers

5. Points are plotted to represent any outliers

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014

A Nielsen Mobile study in 2008 found that teenagers sent or received about 1,742 text messages per month. A statistics teacher was skeptical about this claim, and collected data from his class on the number of texts they sent in the past 24 hours: 0 7 1 29 25 8 5 1 25

98 9 0 26 8 118 72 0 9252 14 3 3 44 5 42

Prob & Stats

3­4 Percentiles & Box­and­Whisker

October 15, 2014