stats chp 4 - Descriptive Statistics Numerical Summaries...

Info iconThis preview shows pages 1–18. Sign up to view the full content.

View Full Document Right Arrow Icon
Stat 3360 1 Descriptive Statistics Numerical Summaries Chapter 4
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 2 Chapter 4 Numerical summaries Population versus sample Central tendency-location Variation-Spread Graphical displays of dispersion Covariance
Background image of page 2
Stat 3360 3 Descriptive Statistics - Numerical Summaries Central Tendency - location mean or average - center of gravity median - divides sample into halves mode - peaks in frequency distribution
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 4 Mean is the sample mean Sum all the values and divide by number values Notation - Greek symbol - μ for population data n x i Σ x
Background image of page 4
Stat 3360 5 Sample Mean Mean as a balance point. If a fulcrum is placed at the position of the mean, it will balance the histogram.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 6 Caution About the Mean One should be cautious about using the mean when, There are outliers The data is skewed
Background image of page 6
Stat 3360 7 Median The median is the middle value after the data is arranged in ascending order. It is denoted by ( read x tilde). Resistant to outliers or influential observations. x ~
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 8 Steps for Median Rank the data in ascending order Find the middle term The value of this term is the median ~ 1 the value of the th term in a ranked data set 2 n x + ⎛⎞ = ⎜⎟ ⎝⎠
Background image of page 8
Stat 3360 9 Criteria When there is an odd number of elements it is straight forward What happens when there is an even number of elements?
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 10 Example 1 2321 1145 9916 First rank the data (sort ascending)
Background image of page 10
Stat 3360 11 Data Sorted 1 1 1 1 2 2 3 4 5 6 9 9 12 1 13 6.5 22 + ⎛⎞ == ⎜⎟ ⎝⎠ We are looking for the 6.5 th value And which value is that?
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 12 Answer Take the average of the sixth and seventh value for this dataset. ~ 23 5 2.5 22 x + ⎛⎞ == = ⎜⎟ ⎝⎠
Background image of page 12
Stat 3360 13 Mode The observation that occurs with highest frequency Works for both quantitative and qualitative data There can more than one Bimodal Multimodal
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 14 Relationship Between Measures of Central Tendency All are equal when distribution is symmetric Mean and mode alternate depending on direction of skewness
Background image of page 14
Stat 3360 15 Section 4.2 Variability
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Stat 3360 16 Spread Dispersion or Variation Easy measure to calculate is the range Range is difference between highest and lowest values Max minus min
Background image of page 16
Stat 3360 17 Variation Deviation Difference between observation and sample mean Note that the sum of the deviations of a sample is zero Standard deviation is square root of variance
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 18
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/06/2008 for the course STAT STAT 3360 taught by Professor Mcghee during the Spring '08 term at University of Texas at Dallas, Richardson.

Page1 / 63

stats chp 4 - Descriptive Statistics Numerical Summaries...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online