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 is very common. averages

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 9 15 5 8 7 14 5.5 8 15 13 8 7 13 8 7 6 6 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 Words Measurements or Amounts Categories (like Yes or No) - Quantitative - Categorical - Quantitative - 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.

Categorical Discrete Continuous Categorical 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 stem. They look like this: Stem Leaf 1|4 means 14 The smaller digit is the leaf. 1 2 3 5 6 1 4 2 3 8 9 We also need a key. Note: Above as shown are values and . 3, 5, 6, 11, 14, 22, 23, 28, 29

2 4 means 24 1 2 3 4 7 1 5 6 7 8 0 0 1 1 2 4 9 2 7 9 0 1 3 8 1 3 5 4 7 20 2 4 means 2.4 3 4 5 6 7 4 6 6 8 1 4 9 2 0 2