When we collect data from an experiment, it can be “distributed” (spread out) in different ways.

Slides:

Advertisements

Similar presentations

Normal Probability Distributions 1 Chapter 5. Chapter Outline Introduction to Normal Distributions and the Standard Normal Distribution 5.2 Normal.

Advertisements

MA-250 Probability and Statistics Nazar Khan PUCIT Lecture 3.

HS 67 - Intro Health Stat The Normal Distributions

Normal distribution. An example from class HEIGHTS OF MOTHERS CLASS LIMITS(in.)FREQUENCY

HOW TALL ARE APRENDE 8 TH GRADERS? Algebra Statistics Project By, My Favorite Math Teacher In my project I took the heights of 25 Aprende 8 th graders.

Ch. 6 The Normal Distribution

Warm Up Calculate the average Broncos score for the 2013 Season!

Discrete and Continuous Random Variables Continuous random variable: A variable whose values are not restricted – The Normal Distribution Discrete.

Standard Deviation In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts.

Normal Distributions.

Normal Distributions Section Starter A density curve starts at the origin and follows the line y = 2x. At some point on the line where x = p, the.

The Normal distributions BPS chapter 3 © 2006 W.H. Freeman and Company.

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. Statistics The collection, evaluation, and interpretation of data Statistical analysis of measurements can help verify.

Normal Distributions and the Empirical Rule Learning Target: I can use percentiles and the Empirical rule to determine relative standing of data on the.

NOTES The Normal Distribution. In earlier courses, you have explored data in the following ways: By plotting data (histogram, stemplot, bar graph, etc.)

Transformations, Z-scores, and Sampling September 21, 2011.

Continuous Random Variables Continuous Random Variables Chapter 6.

Normal Distributions.

Density Curves Can be created by smoothing histograms ALWAYS on or above the horizontal axis Has an area of exactly one underneath it Describes the proportion.

Tuesday, March 18, 2014MAT Tuesday, March 18, 2014MAT 3122.

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 13-5 The Normal Distribution.

The Normal Curve Packet #23. Normal Curve  Referred to as a bell- shaped curve  Perfect mesokurtic distribution.

MAT 1000 Mathematics in Today's World. Last Time 1.Three keys to summarize a collection of data: shape, center, spread. 2.Can measure spread with the.

The Normal Distribution Chapter 6. Outline 6-1Introduction 6-2Properties of a Normal Distribution 6-3The Standard Normal Distribution 6-4Applications.

Thursday, February 27, 2014MAT 312. Thursday, February 27, 2014MAT 312.

2.1 Density Curves & the Normal Distribution. REVIEW: To describe distributions we have both graphical and numerical tools.  Graphically: histograms,

Has a single peak at the center. Unimodal. Mean, median and the mode are equal and located in the center of the curve. Symmetrical about the mean. Somewhat.

Chapter 5 Normal Probability Distributions. Chapter 5 Normal Probability Distributions Section 5-1 – Introduction to Normal Distributions and the Standard.

Descriptive Statistics for one Variable. Variables and measurements A variable is a characteristic of an individual or object in which the researcher.

Honors Advanced Algebra Presentation 1-6. Vocabulary.

Chapter 4 Lesson 4.4a Numerical Methods for Describing Data

The Normal Distribution Chapter 2 Continuous Random Variable A continuous random variable: –Represented by a function/graph. –Area under the curve represents.

Normal Distribution S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

Density Curves Frequency histogram- uses counts of items in each class Relative frequency histogram- uses percent of observations in each class Density.

11.10 NORMAL DISTRIBUTIONS SWBAT: USE A NORMAL DISTRIBUTION, IDENTIFY LEFT AND RIGHT SKEWS, AND APPLY STANDARD DEVIATIONS TO INTERPRET DATA FROM NORMAL.

The Normal Distribution Represented by a function/graph. Area under the curve represents the proportions of the observations Total area is exactly 1.

Bell Ringer Using all available resources (especially your brain), answer the following: 1. What is normal? 2. What are the three measures of central tendency?

Section 2.1 Density Curves

Normal Probability Distribution

Interpreting Center & Variability.

The Normal Distribution

Unit II: Research Method: Statistics

Average, Median, and Standard Deviation

Chapter 5 Normal Probability Distributions.

Normal Distribution When we collect data from an experiment, it can be “distributed” (spread out) in different ways.

Normal Distributions and the Empirical Rule

Using the Empirical Rule

Interpreting Center & Variability.

Chapter 12 Statistics 2012 Pearson Education, Inc.

Normal Distribution Many things closely follow a Normal Distribution:

Elementary Statistics: Picturing The World

Interpreting Center & Variability.

Interpreting Center & Variability.

Normal Probability Distributions

The Normal Distribution

Normal Probability Distributions

7-7 Statistics The Normal Curve.

Normal Curve 10.3 Z-scores.

10-5 The normal distribution

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.

Sec Introduction to Normal Distributions

The Normal Distribution

Section 13.6 The Normal Curve

Introduction to Normal Distributions

Chapter 5 Normal Probability Distributions.

Chapter 5 Normal Probability Distributions.

Chapter 12 Statistics.

Presentation transcript:

When we collect data from an experiment, it can be “distributed” (spread out) in different ways.

There are many cases where the data tends to be around a central value, equally spread left and right, getting close to a “Normal Distribution.” The yellow histogram shows data that follows closely, not necessarily perfectly, a bell curve.

The Normal Distribution has: Mean = Median = Mode Symmetry about the center 50% of values smaller than the mean and 50% of values greater than the mean

Remember that the Standard Deviation is a measure of how spread out numbers are for a set of data. After you compute the standard deviation for a Normal Distribution, you will find out:

In summary (Empirical Rule): 99.7% We can say that in a Normal Distribution any value is: Likely to be within 1 standard deviation of the mean (68%) Very likely to be within 2 standard deviations of the mean (95%) Almost certain to be within 3 standard deviations of the mean (99.7%)

Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights

Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights

Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights

Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights

Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 3)What percent of students can we expect to have heights less than 1.25 m? How many LHS students are shorter than 1.25 m?

Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 3)What percent of students can we expect to have heights less than 1.25 m? How many LHS students are shorter than 1.25 m? 4)What percent of students can we expect to be taller than 1.7 m? How many LHS students are taller than 1.7 m?

Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 3)What percent of students can we expect to have heights less than 1.25 m? How many students are shorter than 1.25 m? 4)What percent of students can we expect to be taller than 1.7 m? How many LHS students are taller than 1.7 m? 5)What percent of students can we expect to have heights between 0.95 m and 1.85 m? How many LHS students have heights between 0.95 m and 1.85 m?