Suppose you take the SAT test and the ACT test. Not using the chart they provide, can you directly compare your SAT Math score to your ACT math score?

Slides:

Advertisements

Similar presentations

Through Percentiles. Suppose you take the SAT test and the ACT test. Not using the chart they provide, can you directly compare your SAT Math score to.

Advertisements

Percentiles and the Normal Curve

Chapter – 5.4: The Normal Model

How do I use normal distributions in finding probabilities?

AP Statistics HW: p95 22 – 24, 27 (skip part c) Obj: to understand and use a z-score and standard normal distribution Do Now: The mean monthly cost of.

Normal Distributions: Finding Values

Z - SCORES standard score: allows comparison of scores from different distributions z-score: standard score measuring in units of standard deviations.

Standard Scores Standard scores, or “z- scores” measure the relation between each score and its distribution.

Standard Normal Distribution The Classic Bell-Shaped curve is symmetric, with mean = median = mode = midpoint.

Active Learning Lecture Slides For use with Classroom Response Systems Probability Distributions.

Did you know ACT and SAT Score are normally distributed?

14.4 The Normal Distribution

Find the indicated z score: z = Find the indicated z score:.6331 z 0 z = –

z-Scores What is a z-Score? How Are z-Scores Useful? Distributions of z-Scores Standard Normal Curve.

Normal Distribution Curves

Chapter 11: Random Sampling and Sampling Distributions

Unit 5 Data Analysis.

Quiz 5 Normal Probability Distribution.

Copyright © Cengage Learning. All rights reserved. 6 Normal Probability Distributions.

Quantitative Methods PSY302 Quiz Chapter Three Review

In 2009, the mean mathematics score was 21 with a standard deviation of 5.3 for the ACT mathematics section. ReferenceReference Draw the normal curve in.

An Introduction to Making Inferences. descriptive statistics – summarize important characteristics of known population data inferential statistics – we.

Topic 3 Z-Scores Unit 5 Topic 3. Explore Lindsay’s class wrote three diploma examinations. The results are shown in the table below. Relative to the other.

Chapter 3 Distributions. Continuous random variables Are numerical variables whose values fall within a range or interval Are measurements Can be described.

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.

AP Statistics Monday, 21 September 2015 OBJECTIVE TSW examine density curves, z-scores, Chebyshev’s Rule, normal curves, and the empirical rule. ASSIGNMENT.

Z Scores. Normal vs. Standard Normal Standard Normal Curve: Most normal curves are not standard normal curves They may be translated along the x axis.

Chapter 6.1 Normal Distributions. Distributions Normal Distribution A normal distribution is a continuous, bell-shaped distribution of a variable. Normal.

Thinking Mathematically Statistics: 12.5 Problem Solving with the Normal Distribution.

Normal Probability Distribution Using Normal Distribution for Probability.

Z-Scores Standardized Scores. Standardizing scores With non-equivalent assessments it is not possible to develop additive summary statistics. –e.g., averaging.

Chapter 5: z-Scores x = 76 (a) X = 76 is slightly below average x = 76 (b) X = 76 is slightly above average 3 70 x = 76 (c) X = 76 is far.

7.4 Normal Distributions Part II p GUIDED PRACTICE From Yesterday’s notes A normal distribution has mean and standard deviation σ. Find the indicated.

Standardized Scores (Z-Scores) By: David Ruff. Z-Score Defined The number of standard deviations a raw score (individual score) deviates from the mean.

2.2 Standard Normal Calculations

What if.... You recently finished taking a test that you received a score of 90 It was out of 200 points The highest score was 110 The average score was.

APPLICATIONS OF THE NORMAL DISTRIBUTION

Thinking Mathematically Statistics: 12.4 The Normal Distribution.

Chapter 5 Normal Probability Distributions. Chapter 5 Normal Probability Distributions Section 5-3 – Normal Distributions: Finding Values A.We have learned.

Honors Advanced Algebra Presentation 1-6. Vocabulary.

NOTES: page 26. Suppose you take the SAT test and the ACT test. Not using the chart they provide, can you directly compare your SAT Math score to your.

Chapter 4 Lesson 4.4a Numerical Methods for Describing Data

3.5 Applying the Normal Distribution – Z Scores Example 1 Determine the number of standard deviations above or below the mean each piece of data is. (This.

Z-Scores. Histogram A bar chart of a frequency distribution. 0 — 2 1 — 3 2 — 0 3 — 2 4 — 4 5 — 3 6 — 3 7 — 5 8 — 3 9 — 2 10—2.

 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)

Chapter 3 Modeling Distributions of Data Page 101.

6.2 – USE NORMAL DISTRIBUTIONS Unit 6 – Data Analysis and Probability.

MATH 1107 Elementary Statistics Lecture 5 The Standard Deviation as a Ruler.

1 Standard Normal Distribution Curve Standard Score.

 The heights of 16-year-old males are normally distributed with mean 68 inches and a standard deviation 2 inches. Determine the z-score for: ◦ 70.

Characteristics of Normal Distribution symmetric with respect to the mean mean = median = mode 100% of the data fits under the curve.

Unit 2: Modeling Distributions of Data of Data. Homework Assignment For the A: 1, 3, 5, Odd, 25 – 30, 33, 35, 39 – 59 Odd and 54, 63, 65 – 67,

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

Chapter 3 Distributions.

Interpreting Center & Variability.

Normal Distribution.

Describing Location in a Distribution

Standard and non-standard

Interpreting Center & Variability.

Interpreting Center & Variability.

Calculating the median

Interpreting Center & Variability.

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.

MATH 2311 Section 4.3.

Normal Distributions and Z-Scores

Normal Distributions and the Empirical Rule

Normal Distribution.

Homework: pg. 500 #41, 42, 47, )a. Mean is 31 seconds.

Algebra 2 Normal Curve Analysis Practice

Objectives The student will be able to:

Presentation transcript:

Suppose you take the SAT test and the ACT test. Not using the chart they provide, can you directly compare your SAT Math score to your ACT math score? Why or why not? We need to standardized these scores so that we can compare them.

z score Standardized score Has  = 0 &  = 1

Let’s explore... Suppose the mean and standard deviation of a distribution are  = 50 &  = 5. If the x-value is 55, what is the z-score? If the x-value is 45, what is the z-score? If the x-value is 60, what is the z-score? So what does the z-score tell you? 1 2

What do these z scores mean?  below the mean 1.8  above the mean 6.1  above the mean 4.3  below the mean

Jonathan wants to work at Utopia Landfill. He must take a test to see if he is qualified for the job. The test has a normal distribution with  = 45 and  = 3.6. In order to qualify for the job, a person can not score lower than 2.5 standard deviations (z score) below the mean. Jonathan scores 35 on this test. Does he get the job? No, he scored 2.78 SD below the mean

Sally is taking two different math achievement tests with different means and standard deviations. The mean score on test A was 56 with a standard deviation of 3.5, while the mean score on test B was 65 with a standard deviation of 2.8. Sally scored a 62 on test A and a 69 on test B. On which test did Sally score the best? She did better on test A.