1. Descriptive Statistics Chapter 2

2. § 2.1 Frequency Distributions and Their Graphs

3. Larson & Farber, Elementary Statistics: Picturing the World, 3e 3 A frequency histogram is a bar graph that represents the frequency distribution of a data set. Frequency Histogram 1.The horizontal scale is quantitative and measures the data values. 2.The vertical scale measures the frequencies of the classes. 3.Consecutive bars must touch. Class boundaries are the numbers that separate the classes without forming gaps between them. The horizontal scale of a histogram can be marked with either the class boundaries or the midpoints.

4. Larson & Farber, Elementary Statistics: Picturing the World, 3e 4 Class Boundaries Example : Find the class boundaries for the “ Ages of Students” frequency distribution. 49.5  57.5 41.5  49.5 33.5  41.5 25.5  33.5 17.5  25.5 The distance from the upper limit of the first class to the lower limit of the second class is 1. Half this distance is 0.5. Class Boundaries 50 – 572 3 4 8 13 42 – 49 34 – 41 26 – 33 18 – 25 Frequency, fClass Ages of Students

5. Larson & Farber, Elementary Statistics: Picturing the World, 3e 5 Frequency Histogram Example: Draw a frequency histogram for the “ Ages of Students” frequency distribution. Use the class boundaries. 2 3 4 8 13 Broken axis Ages of Students 10 8 6 4 2 0 Age (in years) f 12 14 17.5 25.533.541.549.557.5

6. Larson & Farber, Elementary Statistics: Picturing the World, 3e 6 A frequency polygon is a line graph that emphasizes the continuous change in frequencies. Frequency Polygon 1.The horizontal scale is the class midpoints. 2.The vertical scale measures the frequencies of the classes. 3.All points are connected with a straight line.

7. Larson & Farber, Elementary Statistics: Picturing the World, 3e 7 Frequency Polygon A frequency polygon is a line graph that emphasizes the continuous change in frequencies. Broken axis Ages of Students 10 8 6 4 2 0 Age (in years) f 12 14 13.521.529.537.545.553.561.5 Midpoints Line is extended to the x - axis.

8. Larson & Farber, Elementary Statistics: Picturing the World, 3e 8 Relative Frequency Histogram A relative frequency histogram has the same shape and the same horizontal scale as the corresponding frequency histogram. 0.4 0.3 0.2 0.1 0.5 Ages of Students 0 Age (in years) Relative frequency (portion of students) 17.5 25.533.541.549.557.5 0.433 0.267 0.133 0.1 0.067

9. Larson & Farber, Elementary Statistics: Picturing the World, 3e 9 Cumulative Frequency Graph A cumulative frequency graph or ogive, is a line graph that displays the cumulative frequency of each class at its upper class boundary. 17.5 Age (in years) Ages of Students 24 18 12 6 30 0 Cumulative frequency (portion of students) 25.533.541.549.557.5 The graph ends at the upper boundary of the last class.

10. Larson & Farber, Elementary Statistics: Picturing the World, 3e 10 Homework Monday HW Pg 43-47 #8,19-22,25,29 Tuesday HW 7, 18, 27, 33

11. Larson & Farber, Elementary Statistics: Picturing the World, 3e 11 Homework Pg 43-47 # 7, 18, 28, 36 7True 18a)44 b) 70 inches 28 and 36 see scans