1. Histograms Lecture 18 Sec. 4.4.4 Tue, Feb 17, 2004

2. Histograms Histogram – A display of continuous quantitative data in which the data are divided into classes and rectangles represent the frequencies of the classes. Histogram – A display of continuous quantitative data in which the data are divided into classes and rectangles represent the frequencies of the classes.

3. Drawing Histograms Use Data Set 1 on p. 184. Use Data Set 1 on p. 184. Find the maximum value, the minimum value, and the range. Find the maximum value, the minimum value, and the range. Maximum = 51 Maximum = 51 Minimum = 32 Minimum = 32 Range = Max – Min = 51 – 32 = 19. Range = Max – Min = 51 – 32 = 19.

4. Drawing Histograms Divide the data into classes of equal width. Divide the data into classes of equal width. The classes must not overlap. The classes must not overlap. Choose a convenient starting point. Choose a convenient starting point. Choose a convenient class width. Choose a convenient class width. Write the endpoints of each class. Write the endpoints of each class.

5. Drawing Histograms Starting point = 30. Starting point = 30. Class width = 5. Class width = 5. Classes: Classes: 30 up to 35 (but not including 35). 30 up to 35 (but not including 35). 35 up to 40. 35 up to 40. 40 up to 45. 40 up to 45. 45 up to 50. 45 up to 50. 50 up to 55. 50 up to 55.

6. Drawing Histograms We may denote the classes in either of two ways. We may denote the classes in either of two ways. Interval notation: [low, high) Interval notation: [low, high) [30, 35), [30, 35), [35, 40), [35, 40), [40, 45), etc. [40, 45), etc. [ and ] mean “include endpoints.” [ and ] mean “include endpoints.” ( and ) mean “exclude endpoints.” ( and ) mean “exclude endpoints.”

7. Drawing Histograms Range notation: low – high Range notation: low – high 30 – 34, 30 – 34, 35 – 39, 35 – 39, 40 – 44, etc. 40 – 44, etc. This notation does not indicate whether the endpoints are included. This notation does not indicate whether the endpoints are included. Therefore, be sure the endpoints do not overlap. Therefore, be sure the endpoints do not overlap.

8. Drawing Histograms Count the number of observations in each class. This is the frequency of the class. Count the number of observations in each class. This is the frequency of the class. ClassFrequency [30, 35) 1 [35, 40) 2 [40, 45) 8 [45, 50) 7 [50, 55) 2

9. Drawing Histograms Draw horizontal and vertical axes. Draw horizontal and vertical axes. On the horizontal axis, show the class boundaries. On the horizontal axis, show the class boundaries. On the vertical axis, show uniform reference points representing frequencies apropos to the data. On the vertical axis, show uniform reference points representing frequencies apropos to the data. For example, 0, 2, 4, … For example, 0, 2, 4, …

10. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

11. Drawing Histograms Over each class, draw a rectangle whose height is the frequency of that class. Over each class, draw a rectangle whose height is the frequency of that class.

12. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

13. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

14. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

15. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

16. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

17. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

18. Drawing Histograms 303540455055 Age 2 4 6 8 0 Frequency

19. Guidelines Never use too few or too many classes. Never use too few or too many classes. Usually 5 to 12 classes is about right. Usually 5 to 12 classes is about right. Use simple round numbers for the class boundaries. Use simple round numbers for the class boundaries. Mark off the vertical axis uniformly, showing regular reference points, not the actual frequencies. Mark off the vertical axis uniformly, showing regular reference points, not the actual frequencies. Frequencies must start at 0. Frequencies must start at 0.

20. Let’s Do It! Let’s do it! 4.14, p. 224 – Histogram of Household Income. Let’s do it! 4.14, p. 224 – Histogram of Household Income. Let’s do it! 4.16, p. 226 – Matching Shapes to Characteristics. Let’s do it! 4.16, p. 226 – Matching Shapes to Characteristics.

21. Example See Example 4.10, p. 227 – Histogram versus Bar Graph. See Example 4.10, p. 227 – Histogram versus Bar Graph.

22. Histograms on the TI-83 See page 263 for more detailed instructions. See page 263 for more detailed instructions. Enter the data into list L 1. Enter the data into list L 1. {45, 41, 51, …, 37}  L 1 {45, 41, 51, …, 37}  L 1 Press STAT PLOT Press STAT PLOT Turn Plot1 On. Turn Plot1 On. Select Histogram Type. Select Histogram Type. Specify List L 1. Specify List L 1.

23. Histograms on the TI-83 Press WINDOW Press WINDOW Set Xmin to the starting point. Set Xmin to the starting point. Set Xmax to the last endpoint. Set Xmax to the last endpoint. Set Xscl to the class width. Set Xscl to the class width. Set Ymin to 0. Set Ymin to 0. Set Ymax to the maximum frequency. Set Ymax to the maximum frequency. Press GRAPH Press GRAPH The histogram appears. The histogram appears.

24. Frequency Distributions on the TI-83 After getting the histogram, press TRACE. After getting the histogram, press TRACE. The display shows the first class and its frequency. The display shows the first class and its frequency. Use the left arrow to see the other class frequencies. Use the left arrow to see the other class frequencies.

25. Assignment Page 227: Exercises 30 – 38. Page 227: Exercises 30 – 38. Page 249: Exercises 68, 69. Page 249: Exercises 68, 69.