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

BrainPop• Graphs

Types of Data

• Categorical Data – Describes a particular quality or characteristic. It can be divided into categories.

– i.e. color of eyes or types of ice cream

• Quantitative Data – Contains a numerical value. The information collected is termed numerical data.– Discrete – Takes exact number values and is often the result of counting.• i.e. number of TVs or number of houses on a street

– Continuous – Takes numerical values within a certain range and is often a result of measuring.• i.e. the height of seniors or the weight of freshman

Section 5A – Describing Data

Classify these as categorical, quantitative discrete or quantitative continuous:

a) The number of heads obtained when 3 coins are tossed.

b) The brand of toothpaste used by the students in our IB Math Studies class.

c) The heights of a group of 15 year old teenagers.

Organizing Categorical Data

Tally and Frequency Table

Section 5B – Presenting and Interpreting Data

Displaying Categorical Data:

Vertical Column Graph

Displaying Categorical Data:

Horizontal Bar Chart

Displaying Categorical Data:

Pie Chart

Displaying Categorical Data:

Segment Bar Chart

Organizing Discrete Quantitative Data

Tally and Frequency Table

Displaying Discrete Quantitative Data:

Dot plot

Displaying Discrete Quantitative Data:

Stemplot

Displaying Discrete Quantitative Data:

Column Graph

On a Piece of Paper:

–Make a Tally and Frequency Table for the Pea Problem With Fertilizer data (Page 113).

– Once completed, compare your results with classmates.

Open Autograph:

- Use the data obtained in your Tally and Frequency table for peas with fertilizer to create a Dot Plot and Column Graph.

By placing a curve over a column graph or dot plot you can describe the distribution of a data set.

Symmetric Distribution

Positively Skewed Distribution

Negatively Skewed Distribution

Outliers

• Data values that are either much larger or much smaller than the general body of data.

• Outliers appear separated from the body of data on a frequency graph.

24 families were surveyed to find the number of people in the family. The results are:

5, 9, 4, 4, 4, 5, 3, 4, 6, 8, 8, 5, 7, 6, 6, 8, 6, 9, 10, 7, 3, 5, 6, 6

a) Is this data discrete or continuous?b) Construct a frequency table for the data.c) Display the data using a column graph.d) Describe the shape of the distribution. Are there any

outliers?e) What percentage of families have 5 or fewer people in

them?

Problem 1

Homework• Exercise 5A, pg 111– #1

• Exercise 5B, pg 116– #2, 4, 5