Transcript An Introduction to Statistics

An Introduction to
Statistics
Slideshow 51, Mathematics
Mr Richard Sasaki
Room 307
Objectives
• Understand the purpose of statistics
• Be able to calculate some simple
averages
• Know the difference between discrete
and continuous numerical data
• Be able to construct stem and leaf
diagrams
Statistics
What is statistics?
Statistics is all about working with and analysing
data. Data is a collection of numbers or values.
Surveys, exams, polls and interviews are
common ways to collect large amounts of data.
We can then make calculations with this data.
Calculating averages is very common.
Averages
If we have 5 pieces of numerical data, 7, 3, 5, 3, 2…
What is the average?
Average has three different principles.
Mean
Mean is the total of the numbers added together,
divided by how many numbers there are.
7+3+5+3+2 =4
5
Averages
Median
Median is the middle value when they are placed
in order.
7, 3, 5, 3, 2 ⇒ 2, 3, 3, 5, 7
∴ Median: 3
Note: It doesn’t matter if you place them in
ascending order or descending order.
Ascending - Least to greatest.
Descending - Greatest to least.
If there is an even number of pieces of data, the
median is the mean of the two middle values.
Averages
Mode
Mode is the most commonly appearing piece of
data.
7, 3, 5, 3, 2 ⇒ Mode: 3
(There are more 3s than any other value.)
Range
Range isn’t an average but it’s useful. This is the
difference between the greatest and least value.
7, 3, 5, 3, 2 ⇒ 7 − 2 = 5
Answers
8
8
8
7
9
7
15
13
6
6
15
14
13
8
5
5.5
8
7
6
All items appear exactly once.
There are two, 5, & 14
9.5
9.5
Statistics
Statistics is all about looking at data. There are
different types of data. Data can be…
• Numbers - Quantitative
• Words - Categorical
• Measurements or Amounts - Quantitative
• Categories (like Yes or No) - Categorical
These are divided into categorical or quantitative
(numeric).
Note: Data with numbers is quantitative, data with
words or letters is categorical.
Quantitative Data
There are two main types of quantitative
(numerical) data, discrete and continuous.
Discrete data has clear gaps between it. For
example, the number of children someone has is
discrete data. You can have 1 child or 2 children,
but not 2.4 children.
Continuous data has no gaps. Someone’s height is
an example. You could be 168.2893 … 𝑐𝑚 tall.
Discrete
Categorical
Categorical
Continuous
Discrete
Continuous
We often just round to the nearest 𝑐𝑚, but if we
consider exact height, it’s continuous.
No, it can of course be very close but its molecular
structure would prevent this. This is the nature of
continuous data measurements.
Brown, Blonde, Pink
Cat, Rabbit, Sheep
Maebashi, Sapporo, Pyongyang
Petrol, Diesel, Hydrogen
2, 3, 6
Yes (biased)
No (fair)
No (fair)
Yes (biased)
Stem and Leaf Diagrams
Stem and Leaf diagrams are used for analysing
quantitative data. They are compact and are good for
large numbers of data. Simple cases consider two
digits.
The larger digit is the
They look like this:
stem.
Stem Leaf 1|4 means 14 The smaller digit is
0 356
the leaf.
1 14
We also need a key.
2 2389
Note: Above as shown are values 3, 5, 6,11,14, 22,
23, 28, and 29.
0
1
2
3
4
2 4 means 24
7
15678
0011249
279
0138
1
5
7
3
4
5
6
7
2 4 means 2.4
4668
14
9
2
02
3
4
20