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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