A P STATISTICS LESSON 2 – 2 STANDARD NORMAL CALCULATIONS.

Slides:

Advertisements

Similar presentations

The Normal Distribution

Advertisements

Exam One Review Quiz Psy302 Quantitative Methods.

Standard Normal Calculations 2.2 b cont. Target Goal: I can standardize individual values and compare them using a common scale Hw: pg 105: 13 – 15, pg.

Normal Distribution; Sampling Distribution; Inference Using the Normal Distribution ● Continuous and discrete distributions; Density curves ● The important.

Topic 3 The Normal Distribution. From Histogram to Density Curve 2 We used histogram in Topic 2 to describe the overall pattern (shape, center, and spread)

The Normal Curve Z Scores, T Scores, and Skewness.

Standard Deviation A measure of variability

Did you know ACT and SAT Score are normally distributed?

Chapter 11: Random Sampling and Sampling Distributions

Continuous Probability Distributions A continuous random variable can assume any value in an interval on the real line or in a collection of intervals.

Statistics Normal Probability Distributions Chapter 6 Example Problems.

BPT 2423 – STATISTICAL PROCESS CONTROL.  Frequency Distribution  Normal Distribution / Probability  Areas Under The Normal Curve  Application of Normal.

§ 5.2 Normal Distributions: Finding Probabilities.

Chapter Six Normal Curves and Sampling Probability Distributions.

Warm-Up If the variance of a set of data is 12.4, what is the standard deviation? If the standard deviation of a set of data is 5.7, what is the variance?

Introduction to Summary Statistics

Chapter 6 The Standard Deviation as a Ruler and the Normal Model.

The Normal Curve, Standardization and z Scores Chapter 6.

Describing Behavior Chapter 4. Data Analysis Two basic types  Descriptive Summarizes and describes the nature and properties of the data  Inferential.

Density Curves and the Normal Distribution.

Aim: what is the normal distribution? Do Now: Two sets of data given Find the mean.

Normal Distributions.  Symmetric Distribution ◦ Any normal distribution is symmetric Negatively Skewed (Left-skewed) distribution When a majority of.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1.

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

Statistics for Psychology!

AP STATISTICS LESSON 1 – 2 (DAY 3) LINEAR TRANSFORMATIONS AND COMPARING DISTRIBUTIONS.

Chapter 2: Describing Location In a Distribution Section 2.1 Measures of Relative Standing And Density Curves.

Normal Curves Often good representation of real data Often good approximations of chance outcomes.

The Standard Normal Distribution Section 5.2. The Standard Score The standard score, or z-score, represents the number of standard deviations a random.

 Two basic types Descriptive  Describes the nature and properties of the data  Helps to organize and summarize information Inferential  Used in testing.

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

Correlation. Correlation is a measure of the strength of the relation between two or more variables. Any correlation coefficient has two parts – Valence:

: An alternative representation of level of significance. - normal distribution applies. - α level of significance (e.g. 5% in two tails) determines the.

BASIC STATISTICAL CONCEPTS Chapter Three. CHAPTER OBJECTIVES Scales of Measurement Measures of central tendency (mean, median, mode) Frequency distribution.

Section 2.4: Measures of Spread. Example: Using the number of days of vacation for 6 students, find the range, variance and standard deviation. (this.

Thinking Mathematically Statistics: 12.4 The Normal Distribution.

Chapter 9 – The Normal Distribution Math 22 Introductory Statistics.

Standard Normal Calculations 2.2 Standard Normal Calculations 2.2 Target Goal: I can standardize individual values and compare them using a common scale.

© 2008 McGraw-Hill Higher Education The Statistical Imagination Chapter 5. Measuring Dispersion or Spread in a Distribution of Scores.

Chapter 4 Lesson 4.4a Numerical Methods for Describing Data

 A standardized value  A number of standard deviations a given value, x, is above or below the mean  z = (score (x) – mean)/s (standard deviation)

Normal Probability Distributions Chapter 5. § 5.2 Normal Distributions: Finding Probabilities.

2.2 Standard Normal Calculations. Empirical vs. Standardizing Since all normal distributions share common properties, we have been able to use the

Statistics Josée L. Jarry, Ph.D., C.Psych. Introduction to Psychology Department of Psychology University of Toronto June 9, 2003.

Normal Distribution SOL: AII Objectives The student will be able to:  identify properties of normal distribution  apply mean, standard deviation,

Z-scores, normal distribution, and more.  The bell curve is a symmetric curve, with the center of the graph being the high point, and the two sides on.

Lesson Topic: The Mean Absolute Deviation (MAD) Lesson Objective: I can…  I can calculate the mean absolute deviation (MAD) for a given data set.  I.

Measures of Variation. Variation Variation describes how widely data values are spread out about the center of a distribution.

Section 2 Standard Units and Areas under the Standard Normal Distribution.

CHAPTER 2 Modeling Distributions of Data

Standard Normal Calculations

Finding z-scores using Chart

Analyzing One-Variable Data

Sample vs Population comparing mean and standard deviations

12/1/2018 Normal Distributions

Standard Normal Calculations 2.2 b cont.

6-3 Standard Units Areas under Normal Distributions

Aim: what is the normal distribution?

Year-3 The standard deviation plus or minus 3 for 99.2% for year three will cover a standard deviation from to To calculate the normal.

2.1 Density Curves and the Normal Distributions

Sampling Distribution of a Sample Proportion

Section 2.2 Standard Normal Calculations

Use the graph of the given normal distribution to identify μ and σ.

CHAPTER 2 Modeling Distributions of Data

MATH 2311 Section 4.3.

The Normal Distribution

Normal Distribution A normal distribution, sometimes called the bell curve, is a distribution that occurs naturally in many situations. For example, the bell.

The Practice of Statistics

Standard Deviation!.

Introduction to Behavioral Statistics

Presentation transcript:

A P STATISTICS LESSON 2 – 2 STANDARD NORMAL CALCULATIONS

ESSENTIAL QUESTION: How is the Standard Normal Curve used to find information about data? Objectives: To find Z scores of data from normal distributions. To use the standard normal curve to help answer real world problems.

Standard Normal Distributions All normal distributions are the same if we measure in units of size σ about a mean μ as center. Changing to these units is called standardizing the data.

Standardizing and Z - scores If x is an observation from a distribution that has mean μ and standard deviation σ, the standardized value of x is Z = x – μ A standardized value is often called a z – score. σ

Z - Scores Tells us how many standard deviations the original observation falls away from the mean, and which direction. Observations larger than the mean are positive when standardized, and observations smaller than the mean are negative. If the variable we standardize has a normal distribution, standardizing does more than give a common scale. It makes all normal distributions into a single distribution, and this distribution is still normal.

Standard Normal Distribution The standard normal distribution is the normal distribution N( 0, 1 ) with mean 0 and standard deviation 1 If a variable x has any normal distribution N( μ, σ ) with mean μ and standard deviation σ, then the standard variable has the standard normal distribution. Z = x - μ σ

Normal Distribution Calculations