Describing Quantitative Data with Numbers Part 2

1.3 B

Five-Number Summary The five number summary consists of the

minimum value, the first quartile, the median, the third quartile and the maximum value in the data set.

It is written in order: min, Q1, M, Q3, max

It essentially divides the data up into fourths. 25% of the data values lie in the intervals between each number.

Boxplots (Box and Whisker) A graphical representation of the 5 Number Summary

A central box is drawn from the 1st Quartile to the 3rd Quartile

A line in the box represents the Median Lines (called whiskers) extend from the box out to the

lowest and highest observations that are NOT outliers Dots beyond the whiskers indicate observations that are

outliers if any exist (1.5x IQR Rule) Boxplots can be oriented horizontally or vertically The axis parallel to the boxplot should by labeled and

scaled The axis perpendicular may be labeled with a

description of the variable

Number of Home Runs Hit by Barry Bonds

Measure of Spread: Standard Deviation Measures spread by finding the average

distance of the values from the MEAN. The VARIANCE is the average of the distances

squared. They are squared so negative differences (left of mean) don’t cancel out positive differences (right of mean)

The square root of the variance is the standard deviation

The square of the standard deviation is the variance

Variance is in SQUARED units Standard deviation is in the same units as the

data.

Formula for Variance and St. Dev,

2 2 22 1 2

2 2 21 2

( ) ( ) ... ( )Variance of

1

( ) ( ) ... ( )Standard Deviation of

1

nx

nx

x x x x x xx s

n

x x x x x xx s

n

Properties of Standard Deviation It measure the spread about the mean and is

only used with the mean It is always greater than or equal to 0 It has the same units as the data It is highly vulnerable to extreme values

(outliers) and in not a good estimator of spread for skewed data.