1. Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

2. When there is a lot of data values spread over a wide range it is useful to group the data. Normally, there should be between 5 to 15 groups, or classes, of equal width. The classes must cover the range of values and they must not overlap – each data point can only belong to one class. Organize the continuous data into grouped frequency tables. Grouped Discrete or Continuous Organizing Grouped Discrete or Continuous Data

3. Loni made 30 telephone calls one week, The times of her calls, in minutes, were recorded. Organize this information in a grouped frequency table. 3.112.29.68.12.21.2 15.04.821.213.617.322.3 1.54.631.226.77.818.2 35.41.62.95.512.828.3 16.91.35.67.82.36.9 Grouped Discrete or Continuous Organizing Grouped Discrete or Continuous Data

4. Loni made 30 telephone calls one week, The times of her calls, in minutes, were recorded. Organize this information in a grouped frequency table. 3.112.29.68.12.21.2 15.04.821.213.617.322.3 1.54.631.226.77.818.2 35.41.62.95.512.828.3 16.91.35.67.82.36.9 1. Decide on the size and number of classes. 2. Smallest number = 1.2, so classes start at 0. 3. Largest number = 35.4, so classes end at 40. 4. Using a class width of 5, there will be 8 classes in total (40/5 = 8).

5. Loni made 30 telephone calls one week, The times of her calls, in minutes, were recorded. Organize this information in a grouped frequency table. 3.112.29.68.12.21.2 15.04.821.213.617.322.3 1.54.631.226.77.818.2 35.41.62.95.512.828.3 16.91.35.67.82.36.9 Time (t) in MinutesFrequency 0 ≤ t < 510 5 ≤ t < 107 10 ≤ t < 153 15 ≤ t < 204 20 ≤ t < 252 25 ≤ t < 302 30 ≤ t < 351 35 ≤ t < 401

6. Open up page 49 in Oxford and complete Exercise 2C Grouped Discrete or Continuous Organizing Grouped Discrete or Continuous Data

7. To find the upper and lower boundaries of a class, calculate the mean of the upper value from one class and the lower value from the following class. Determining Upper and Lower Boundaries

8. This table shows the heights of flowers in a garden. Write down: A. The upper boundary of the first class. B. The lower boundary of the third class. Height (x) in cmFrequency 0 ≤ x < 105 10 ≤ x < 2012 20 ≤ x < 3021 30 ≤ x < 4015 40 ≤ x < 506 Determining Upper and Lower Boundaries A. (10 + 10) ÷ 2 = 10 B. (20 + 20) ÷ 2 = 20

9. This table shows the number of pairs of shoes of each size sold in a shop one day. Write down: A. The upper boundary of the first class and the last class. B. The lower boundary of the first class and the fourth class. Determining Upper and Lower Boundaries A.(19 + 20) ÷ 2 = 19.5 (44 + 45) ÷ 2 = 44.5 B.(14 + 15) ÷ 2 = 14.5 (29 + 30) ÷ 2 = 29.5 Shoe SizeFrequency 15-193 20-249 25-2912 30-3422 35-3945 40-4431

10. Open up page 51 in Oxford and complete Exercise 2D Determining Upper and Lower Boundaries

11. Consider the weights of students in a rugby training squad. Weight Interval Frequency 50  w < 60 2 60  w < 70 7 70  w < 80 9 80  w < 90 5 90  w < 100 3

12. Each group is called a class. The size of the grouping is called the class interval. The class interval must be the same throughout the table. It is generally a good idea to have 5 to 10 classes. Weight Interval Frequency 50  w < 60 2 60  w < 60 7 70  w < 60 9 80  w < 60 5 90  w < 100 3

13. Provides a useful way to visually represent data. To draw, find the lower and upper boundaries of the classes and draw bars between these boundaries. There should be no spaces between the bars. Frequency Histogram

15. Weight Interval Frequency 50  w < 60 2 60  w < 60 7 70  w < 60 9 80  w < 60 5 90  w < 100 3 Frequency Histogram

16. Remember, for continuous data, the Column Graph is called a Frequency Histogram and the bars must be of equal widths and touching.

17. The weights of parcels sent on a given day from a post office were, in kg: 2.9, 4.0, 1.6, 3.5, 2.9, 3.4, 3.2, 5.2, 4.6, 3.1, 2.8, 3.7, 4.9, 3.4, 1.3, 2.5, 2.2 Practice

18. Make a Frequency Table and a Histogram for the post office data. Weight Frequency 1  w <2 2  w <3 3  w <4 4  w <5 5  w <6

19. Results