Variability.

Slides:



Advertisements
Similar presentations
Describing Distributions with Numbers
Advertisements

Class Session #2 Numerically Summarizing Data
AP Statistics Chapter 16. Discrete Random Variables A discrete random variable X has a countable number of possible values. The probability distribution.
Looking at data: distributions - Describing distributions with numbers IPS chapter 1.2 © 2006 W.H. Freeman and Company.
Descriptive Statistics Statistical Notation Measures of Central Tendency Measures of Variability Estimating Population Values.
Jan Shapes of distributions… “Statistics” for one quantitative variable… Mean and median Percentiles Standard deviations Transforming data… Rescale:
Rules for means Rule 1: If X is a random variable and a and b are fixed numbers, then Rule 2: If X and Y are random variables, then.
Variability Measures of spread of scores range: highest - lowest standard deviation: average difference from mean variance: average squared difference.
Wednesday, October 3 Variability. nominal ordinal interval.
VARIABILITY. PREVIEW PREVIEW Figure 4.1 the statistical mode for defining abnormal behavior. The distribution of behavior scores for the entire population.
1 Chapter 4: Variability. 2 Variability The goal for variability is to obtain a measure of how spread out the scores are in a distribution. A measure.
Variability Ibrahim Altubasi, PT, PhD The University of Jordan.
Mean, Variance, and Standard Deviation for Grouped Data Section 3.3.
Anthony J Greene1 Dispersion Outline What is Dispersion? I Ordinal Variables 1.Range 2.Interquartile Range 3.Semi-Interquartile Range II Ratio/Interval.
Variability The goal for variability is to obtain a measure of how spread out the scores are in a distribution. A measure of variability usually accompanies.
Measures of Variability James H. Steiger. Overview Discuss Common Measures of Variability Range Semi-Interquartile Range Variance Standard Deviation Derive.
Why is the study of variability important? Allows us to distinguish between usual & unusual values In some situations, want more/less variability –scores.
Chapter 4 Variability. Variability In statistics, our goal is to measure the amount of variability for a particular set of scores, a distribution. In.
Measures of Variability Objective: Students should know what a variance and standard deviation are and for what type of data they typically used.
Measures of Variability. Variability Measure of the spread or dispersion of a set of data 4 main measures of variability –Range –Interquartile range –Variance.
Chapter 4 Numerical Methods for Describing Data. Parameter - Fixed value about a population Typical unknown Suppose we want to know the MEAN length of.
Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 3 Section 2 – Slide 1 of 27 Chapter 3 Section 2 Measures of Dispersion.
Rules for Means and Variances. Rules for Means: Rule 1: If X is a random variable and a and b are constants, then If we add a constant a to every value.
Why is the study of variability important? Allows us to distinguish between usual & unusual values In some situations, want more/less variability –medicine.
Why is the study of variability important? Allows us to distinguish between usual & unusual values In some situations, want more/less variability –scores.
3 common measures of dispersion or variability Range Range Variance Variance Standard Deviation Standard Deviation.
Review: Measures of Dispersion Objectives: Calculate and use measures of dispersion, such as range, mean deviation, variance, and standard deviation.
Chapter 4: Variability. Variability Provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together.
Statistics in IB Biology Error bars, standard deviation, t-test and more.
Chapter 5: Measures of Dispersion. Dispersion or variation in statistics is the degree to which the responses or values obtained from the respondents.
PROBABILITY AND STATISTICS WEEK 4 Onur Doğan. Random Variable Random Variable. Let S be the sample space for an experiment. A real-valued function that.
AP Statistics Chapter 16. Discrete Random Variables A discrete random variable X has a countable number of possible values. The probability distribution.
LINEAR TRANSFORMATION RULE When adding a constant to a random variable, the mean changes but not the standard deviation. When multiplying a constant to.
2.4 Measures of Variation Coach Bridges NOTES. What you should learn…. How to find the range of a data set How to find the range of a data set How to.
Variability Introduction to Statistics Chapter 4 Jan 22, 2009 Class #4.
6.2 Transforming and Combining Random Variables Objectives SWBAT: DESCRIBE the effects of transforming a random variable by adding or subtracting a constant.
Lecture 7: Bivariate Statistics. 2 Properties of Standard Deviation Variance is just the square of the S.D. If a constant is added to all scores, it has.
Unit 1 Mr. Lang’s AP Statistics Power point. Homework Assignment 4 For the A: 1, 3, 5, 7, 8, Odd, 27 – 32, 37 – 59 Odd, 60, 69 – 74, 79 – 105 Odd.
Chapter 4 Variability PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J Gravetter and Larry.
Measures of Dispersion
Numerical Methods for Describing Data
Variability.
__________.
Chapter 6: Random Variables
Describing Location in a Distribution
The Standard Deviation as a Ruler and the Normal Model
Variability.
Variability.
Variability.
Chapter 16.
STA 291 Spring 2008 Lecture 5 Dustin Lueker.
STA 291 Spring 2008 Lecture 5 Dustin Lueker.
Describing Data with Numerical Measures
Variability.
Expectation And Variance of Random Variables
Chapter 13 Group Differences
Discrete Distributions
How to describe a graph Otherwise called CUSS
Chapter 1 Warm Up .
Discrete Distributions
Linear Transformations and Standardized Scores
Measures of Center.
Discrete Distributions.
Sample Standard Deviation
Variability.
Discrete Distributions
Variability.
Combining Random Variables
Daily Warm-up Tuesday, April 29th
Presentation transcript:

Variability

Why is the study of variability important? Allows us to distinguish between usual & unusual values In some situations, want more/less variability scores on standardized tests time bombs medicine

Measures of Variability range (max-min) interquartile range (Q3-Q1) deviations variance standard deviation Lower case Greek letter sigma

Suppose that we have these data values: 24 34 26 30 37 16 28 21 35 29 Find the mean. Find the deviations. What is the sum of the deviations from the mean?

24 34 26 30 37 16 28 21 35 29 Square the deviations: Find the average of the squared deviations:

The average of the deviations squared is called the variance. parameter statistic Population Sample

Calculation of variance of a sample df

A standard deviation is a measure of the average deviation from the mean.

Calculation of standard deviation

Degrees of Freedom (df) n deviations contain (n - 1) independent pieces of information about variability

Use calculator

Which measure(s) of variability is/are resistant? IQR

Activity

Linear transformation rule When multiplying or adding a constant to a random variable, the mean changes by both. When multiplying or adding a constant to a random variable, the standard deviation changes only by multiplication. Formulas:

An appliance repair shop charges a $30 service call to go to a home for a repair. It also charges $25 per hour for labor. From past history, the average length of repairs is 1 hour 15 minutes (1.25 hours) with standard deviation of 20 minutes (1/3 hour). Including the charge for the service call, what is the mean and standard deviation for the charges for labor?

Rules for Combining two variables To find the mean for the sum (or difference), add (or subtract) the two means To find the standard deviation of the sum (or differences), ALWAYS add the variances, then take the square root. Formulas: If variables are independent

Bicycles arrive at a bike shop in boxes Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the times for each setup phase are independent with the following means & standard deviations (in minutes). What are the mean and standard deviation for the total bicycle setup times? Phase Mean SD Unpacking 3.5 0.7 Assembly 21.8 2.4 Tuning 12.3 2.7

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com. Inc. All rights reserved.