Summary Elementary Statistics,

3Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 1. Center: A representative or average value that indicates where the middle of the data set is located 2. Variation: A measure of the amount that the values vary among themselves 3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed) 4. Outliers: Sample values that lie very far away from the vast majority of other sample values 5. Time: Changing characteristics of the data over time Important Characteristics of Data 4Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Summarizing Data: Listing and Grouping 5Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Listing Numerical Data • Listing refers to any kind of treatment that preserves the identity of each value, rearrange but not change. • It is the first task in any kind of statistical analysis. • The numbers must be made comprehensible • Sort the data in ascending or descending order to make the mass of information more usable. 6Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 19.2, 19.6,17.3, 19.5, 20.4, 23.5 19.0, 19.4, 18.4, 19.4 Arranging in ascending order 17.3, 18.4, 19.0,19.2,19.4, 19.4,19.5, 19.6, 20.4, 23.5 Example 7Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Dot Diagram • If a set of data consists of relatively few values, many of which are repeated, we simply count how many items each value occurs and then present the result in the form of a table or a dot diagram. • In such a diagram we indicate by means of dots how many times each value occurs. 8Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Dot Diagram • Example1: An audit of twenty tax returns revealed 0, 2, 0, 0, 1, 3, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 1 and 0 mistakes in arithmetic. • Construct a table showing the number of tax returns with 0, 1, 2 and 3 mistakes in arithmetic. • Draw a dot diagram displaying the same information. 9Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Number of tax returns Number of mistakes 12 5 2 1 0 1 2 3 ● ● ● ● ● ● ● ●● ●● ●● ●●● ●●●● 3210 10Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Dot diagram can be modified in various ways: • Instead of dots we can use x’s, ◊’s, *’s. ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊◊ ◊◊ ◊◊ ◊◊◊ ◊◊◊◊ 3210 11Chapter 2. Section 2-1 and 2-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Dots can be aligned horizontally.