Collecting Data Name Number of Siblings Preferred Football Team Star Sign Hand Span

Univariate Data Categorical: a category is recorded

when the data is collected. Examples of categorical data include gender, nationality, occupation.

Numerical: when data is collected a number is recorded.

Univariate Data There are two types of numerical data

Discrete: the numbers recorded are distinct values, often whole numbers and usually the data comes from counting. Examples include number of students in a class, pages in a book.

Continuous: any number on a continuous line is recorded; usually the data is produced by measuring to any desired level of accuracy. Examples include volume of water consumed, life of a battery.

The age of my car is numerical data

TRUE

FALSE

The colour of my car is categorical data

TRUE

FALSE

The number of cars in the car park would be considered numerical & continuous data.

TRUE

FALSE

If I rate my driving experience of some test cars between one and ten, this is considered numerical & discrete data.

TRUE

FALSE

Categorical data has a specific graduated order

TRUE

FALSE

Continuous numerical data can be measured

TRUE

FALSE

If 1 = satisfied, 2 = indifferent & 3 = dissatisfied, I am collecting categorical data

TRUE

FALSE

I cannot get a mean if the data is categorical

TRUE

FALSE

Univariate Data Exercise 1A – 3 & 4

Univariate Data Summarising data

Frequency tables: may be used with both categorical and numerical data. Class intervals are used to group continuous numerical data or to group discrete data where there is a large range of values.

Categorical Data

Favourite team

Frequency

% Frequency

Collingwood 12 12/35 * 100 = 34%

Essendon 5 14%

Bulldogs 15 43%

Carlton 3 9%

Total 35 100%

Categorical DataBar Graph / Column Graph

Preferred Football Team

0

2

4

6

8

10

12

14

16

Collingwood Essendon Bulldogs Carlton

Team

Fre

qu

ency

Percentaged Segmented Bar Chart

Percentaged Segmented Barchart of Favourite Teams

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Team

Perc

en

tag

e F

req

uen

cy

Collingwood

Essendon

Bulldogs

Carlton

Numerical DataDot Plots

Dots plots are used with discrete data and small samples

Number of siblings1 2 3 4 5

Numerical Data

Number of Siblings

Frequency Percentage Frequency

0 2 2/25*100 = 8%

1 4 16%

2 12 48%

3 7 28%

25 100%

Numerical DataHistogram

Numerical Data

Handspan Frequency Percentage Frequency

200 – 209 10 10/30 * 100 = 33%

210 – 219 15 50%

220 – 229 3 10%

230 – 239 2 7%

30 100%

Numerical data Histogram

Mode The mode is the most commonly

occurring category, value or interval.

Numerical DataStem and Leaf Plots

Stem and Leaf Plots display the distribution of numerical data (both discrete and continuous) as well as the actual data values.

An ordered stem and leaf plot is obtained by ordering the numbers in the leaf in ascending order.

A stem and leaf plot should have at least 5 numbers in the stem

Numerical DataStem and Leaf Plots

Stem Leaf 20 1 2 2 5 6 21 0 1 2 22 2 3 8 23 24 0 2

24 0 represents 240

Numerical DataStem and Leaf Plots

Sometimes it may be necessary to split the stems in order to obtain the required number of stems.

Consider the data12 4 6 8 10 16 19 5

Numerical DataDescribing a distribution

Shape Generally one of three types

Symmetric Positively Skewed Negatively Skewed

Numerical DataShape SymmetricSymmetric (same shape either side of the centre)

Numerical DataShape: Positively Skewed

Positively skewed : tails off to the right

Numerical DataShape: Negatively Skewed

Negatively skewed : tails off to the left

Centre The centre is the value which has

the same number of scores above as below.

Spread The maximum and minimum

values should be used to calculate the range.

Range = Maximum Value – Minimum Value

Outliers Outliers are extreme values well

away from the majority of the data

Describe this distribution

Questions from Chapter One

Neat Theory book Neat Practical book Exercise 1B Page 7-8 Questions 2,4,6,8 Exercise 1C Pages 14-15 Questions 1-7 Exercise 1E Page 26 Question 1 Exercise 1D Pages 19-21 Questions 1 - 4 Exercise 1E Pages 26-28 Questions 2,3,4,6,7,8 Chapter One Review Pages 30 – 34