Material Taken From:

Mathematicsfor 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

• 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.

Organizing Grouped Discrete or Continuous Data

Loni made 30 telephone calls one week, The times of her calls,in minutes, were recorded.Organize this information in a grouped frequency table.

3.1 12.2 9.6 8.1 2.2 1.215.0 4.8 21.2 13.6 17.3 22.31.5 4.6 31.2 26.7 7.8 18.235.4 1.6 2.9 5.5 12.8 28.316.9 1.3 5.6 7.8 2.3 6.9

Organizing Grouped Discrete or Continuous Data

Loni made 30 telephone calls one week, The times of her calls,in minutes, were recorded.Organize this information in a grouped frequency table.

3.1 12.2 9.6 8.1 2.2 1.215.0 4.8 21.2 13.6 17.3 22.31.5 4.6 31.2 26.7 7.8 18.235.4 1.6 2.9 5.5 12.8 28.316.9 1.3 5.6 7.8 2.3 6.9

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).

Loni made 30 telephone calls one week, The times of her calls,in minutes, were recorded.Organize this information in a grouped frequency table.3.1 12.2 9.6 8.1 2.2 1.215.0 4.8 21.2 13.6 17.3 22.31.5 4.6 31.2 26.7 7.8 18.235.4 1.6 2.9 5.5 12.8 28.316.9 1.3 5.6 7.8 2.3 6.9

Time (t) in Minutes Frequency0 ≤ t < 5 10

5 ≤ t < 10 710 ≤ t < 15 315 ≤ t < 20 420 ≤ t < 25 225 ≤ t < 30 230 ≤ t < 35 135 ≤ t < 40 1

Open up page 49 in Oxford and complete Exercise 2C

Organizing Grouped Discrete or Continuous Data

• 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

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 cm Frequency0 ≤ x < 10 510 ≤ x < 20 1220 ≤ x < 30 2130 ≤ x < 40 1540 ≤ x < 50 6

Determining Upper and Lower Boundaries

A. (10 + 10) ÷ 2 = 10

B. (20 + 20) ÷ 2 = 20

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 Size Frequency15-19 320-24 925-29 1230-34 2235-39 4540-44 31

Open up page 51 in Oxford and complete Exercise 2D

Determining Upper and Lower Boundaries

Consider the weights of students in a rugby training squad.

Weight Interval Frequency

50 w < 60 260 w < 70 770 w < 80 980 w < 90 590 w < 100 3

• 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 < 60 260 w < 60 770 w < 60 980 w < 60 5

90 w < 100 3

• 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

Frequency Histogram

Weight Interval Frequency

50 w < 60 260 w < 60 770 w < 60 980 w < 60 5

90 w < 100

3

Frequency Histogram

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

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

Make a Frequency Table and a Histogram for the post office data.

Weight Frequency1 w

<22 w

<33 w

<44 w

<55 w

<6

Results