An article on peanut butter reported the following scores (quality ratings on a scale of 0 to 100) for various brands. Construct a comparative stem-and-leaf.

Slides:



Advertisements
Similar presentations
CHAPTER 1 Exploring Data
Advertisements

Statistics for the Social Sciences
B a c kn e x t h o m e Parameters and Statistics statistic A statistic is a descriptive measure computed from a sample of data. parameter A parameter is.
Variation Measures of variation quantify how spread out the data is.
Variance and Standard Deviation. Variance: a measure of how data points differ from the mean Data Set 1: 3, 5, 7, 10, 10 Data Set 2: 7, 7, 7, 7, 7 What.
CHAPTER 2: Describing Distributions with Numbers
AP Statistics Chapters 0 & 1 Review. Variables fall into two main categories: A categorical, or qualitative, variable places an individual into one of.
Descriptive Statistics Used to describe the basic features of the data in any quantitative study. Both graphical displays and descriptive summary statistics.
CHAPTER 2: Describing Distributions with Numbers ESSENTIAL STATISTICS Second Edition David S. Moore, William I. Notz, and Michael A. Fligner Lecture Presentation.
AP Stats BW 9/16 You are going to buy a battery for your video camera. You have 2 companies to choose from and they both claim their batteries will last.
1 Review Descriptive Statistics –Qualitative (Graphical) –Quantitative (Graphical) –Summation Notation –Qualitative (Numerical) Central Measures (mean,
Tuesday August 27, 2013 Distributions: Measures of Central Tendency & Variability.
Descriptive Statistics Measures of Variation. Essentials: Measures of Variation (Variation – a must for statistical analysis.) Know the types of measures.
CHS Statistics 2.5: Measures of Spread
Chapter 6 The Standard Deviation as a Ruler and the Normal Model.
Chapter 12, Part 2 STA 291 Summer I Mean and Standard Deviation The five-number summary is not the most common way to describe a distribution numerically.
Chapter 3: Averages and Variation Section 2: Measures of Dispersion.
© 2013 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems Introductory Statistics: Exploring the World through.
Chapter 5: Measures of Dispersion. Dispersion or variation in statistics is the degree to which the responses or values obtained from the respondents.
An article on peanut butter reported the following scores (quality ratings on a scale of 0 to 100) for various brands. Construct a comparative stem-and-leaf.
Standard Deviation. Two classes took a recent quiz. There were 10 students in each class, and each class had an average score of 81.5.
+ Chapter 1: Exploring Data Section 1.3 Describing Quantitative Data with Numbers The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE.
More Univariate Data Quantitative Graphs & Describing Distributions with Numbers.
Describing Data: Summary Measures. Identifying the Scale of Measurement Before you analyze the data, identify the measurement scale for each variable.
2.4 Measures of Variation The Range of a data set is simply: Range = (Max. entry) – (Min. entry)
Chapter 1 Lesson 7 Variance and Standard Deviation.
Chapter 3 Section 3 Measures of variation. Measures of Variation Example 3 – 18 Suppose we wish to test two experimental brands of outdoor paint to see.
Measures of Variation. Variation Variation describes how widely data values are spread out about the center of a distribution.
Describing Distributions of Quantitative Data
CHAPTER 1 Exploring Data
Chapter 1: Exploring Data
CHAPTER 1 Exploring Data
Do-Now-Day 2 Section 2.2 Find the mean, median, mode, and IQR from the following set of data values: 60, 64, 69, 73, 76, 122 Mean- Median- Mode- InterQuartile.
CHAPTER 1 Exploring Data
CHAPTER 1 Exploring Data
Chapter 5: Describing Distributions Numerically
Warmup What is the shape of the distribution? Will the mean be smaller or larger than the median (don’t calculate) What is the median? Calculate the.
STA 291 Spring 2008 Lecture 5 Dustin Lueker.
STA 291 Spring 2008 Lecture 5 Dustin Lueker.
Teacher Introductory Statistics Lesson 2.4 D
Displaying Distributions with Graphs
Displaying and Summarizing Quantitative Data
CHAPTER 1 Exploring Data
Describing Quantitative Data with Numbers
Chapter 1: Exploring Data
Exploratory Data Analysis
CHAPTER 1 Exploring Data
CHAPTER 1 Exploring Data
Standard Deviation How many Pets?.
Chapter 1: Exploring Data
CHAPTER 1 Exploring Data
Chapter 1: Exploring Data
Chapter 1: Exploring Data
Chapter 1: Exploring Data
CHAPTER 1 Exploring Data
CHAPTER 1 Exploring Data
CHAPTER 1 Exploring Data
CHAPTER 1 Exploring Data
Chapter 1: Exploring Data
The Five-Number Summary
CHAPTER 1 Exploring Data
Chapter 1: Exploring Data
Chapter 1: Exploring Data
Statistics Standard: S-ID
CHAPTER 1 Exploring Data
Chapter 1: Exploring Data
Chapter 1: Exploring Data
CHAPTER 1 Exploring Data
Chapter 1: Exploring Data
Chapter 1: Exploring Data
Presentation transcript:

An article on peanut butter reported the following scores (quality ratings on a scale of 0 to 100) for various brands. Construct a comparative stem-and-leaf plot and compare the graphs. Creamy: Crunchy:

Creamy: Crunchy: Center: The center of the creamy is roughly 45 whereas the center for crunchy is higher at 51. Shape: Both are unimodal but crunchy is skewed to the right while creamy is more symmetric. Spread: The range for creamy and crunchy are equal at. There doesn’t seem to be any gaps in the distribution.

Variation

Which Brand of Paint is better? Why? Brand A Brand B

Standard Deviation It’s a measure of the typical or average deviation (difference) from the mean.

Variance This is the average of the squared distance from the mean.

Which Brand of Paint is better? Why? Brand A Brand B

Does the Average Help? Paint A: Avg = 210/6 = 35 months Paint B: Avg = 210/6 = 35 months They both last 35 months before fading. No help in deciding which to buy.

Consider the Spread Paint A: Spread = 60 – 10 = 50 months Paint B: Spread = 45 – 25 = 20 months Paint B has a smaller variance which means that it performs more consistently. Choose paint B.

Formula for Population Variance = Standard Deviation =

Formula for Sample Variance = Standard Deviation =

Formulas for Variance and St. Deviation Population Sample Variance Standard Deviation Variance Standard Deviation

A more powerful approach to determining how much individual data values vary. This is a measure of the average distance of the observations from their mean. Like the mean, the standard deviation is appropriate only for symmetric data! The use of squared deviations makes the standard deviation even more sensitive than the mean to outliers!

Standard Deviation One way to think about spread is to examine how far each data value is from the mean. This difference is called a deviation. We could just average the deviations, but the positive and negative differences always cancel each other out! So, the average deviation is always 0  not very helpful!

Finding Variance To keep them from canceling out, we square each deviation. Squaring always gives a positive value, so the sum will not be zero! Squaring also emphasizes larger differences – a feature that turns out to be good and bad. When we add up these squared deviations and find their average (almost), we call the result the variance.

Finding Standard Deviation

Let’s look at the data again on the number of pets owned by a group of 9 children. Recall that the mean was 5 pets. Let’s take a graphical look at the “deviations” from the mean:

Let’s Find the Standard Deviation and Variance of the Data Set of Pets Pets x Sum = 16 1 – 5 = -4 3 – 5 = -2 4 – 5 = -1 5 – 5 = 0 7 – 5 = 2 8 – 5 = 3 9 – 5 = 4

Find Variance: This is the “average” squared deviation.

Find the Standard Deviation: This 2.55 is roughly the average distance of the values in the data set from the mean.

Find the Standard Deviation and Variance ValuesDeviationsSquared Deviations

Homework Worksheet