Advanced Higher Statistics

Transcription

1 Advanced Higher Statistics Advanced Higher Statistics - 3 Unit Assessments - Prelim - Investigation - Final Exam (3 Hours) 1

2 Advanced Higher Statistics Handouts - Data Booklet - Course Outlines - Textbooks - Graphical Calculator What do we already know about Statistics? What have you already learned? Do you know any statistics? 2

3 Types of Data Continuous Discrete Data that can take any value. (Within a given range) Data that can only take certain values. Time taken to run five miles (minutes): 34, 23, 87, 35, 83, 200,... Shoe Sizes: 3, 3.5, 4, 4.5, 5, 5.5, 6, Distance travelled to work (miles): 0.3, 0.6, 34.54, 2.3, 29.5,... The number of people in this room: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Bivariate & Univariate Data Univariate - One Variable Bivariate - Two Variables (Bivariate data can be plotted on a scatter graph) 3

4 Univariate Bivariate 4

5 Types of Data As we have different types of data we have to deal with them using different techniques. This leads now into EDA. EDA What does it stand for?! Exploratory Data Analysis What is it then?! 'EDA is detective work - numerical detective work - or graphical detective work. ' (Tukey, 1977) 5

6 Lottery Numbers What patterns and trends can we spot? What data analysis can we perform? How can EDA help us to do some analysis? Can we use our analysis to predict tomorrows numbers? Starter Unscramble the words below to discover some phrases we used yesterday... 1) bear vile 2) cried set 3) I near uta vi 4) batie ravi 5) Alexio payday translators 6

7 - Five Figure Summary - Boxplots - Standard Deviation - Variance Remember: Sigma! Five Figure Summary Min Value Lower Upper Quartile Median Quartile Q Q 1 3 Max Value 7

8 Min Value Lower Upper Quartile Median Quartile Q Q 1 3 Max Value December 2018 Top 11 Advanced Higher Prelim Scores % 56, 61, 64, 66, 69, 72, 74, 74, 77, 79, 79 Range = IQR = SIQR = Sample Standard Deviation (s) from national

9 Variance = Standard Deviation 2 Both describe the spread of the data. Starter Plot this data as a boxplot on the graphical calculator. December 2018 Top 11 Advanced Higher Prelim Scores % 56, 61, 64, 66, 69, 72, 74, 74, 77, 79, 79 9

10 Today we are learning... How to plot a histogram. Histogram I will know if I have been successful if... I understand what is meant by class interval, lower limit and upper limit. I can plot a histogram on the calculator. I can draw a histogram by hand. Lottery Results BB 55 4 and 32 are the most likely to appear. 1-5 and most common interval. Average 5, 14, 22, 34, 43, 49 E O E E E E Less30 Less30 Less30 Above30 Above30 Above30 10

11 Histogram We use a histogram to illustrate continuous data. A bar chart would illustrate discrete data. The bars are together in a histogram, whereas in a bar chart there should be a space between them. 11

12 Sample Spaces Today we are learning... What are samples spaces and how do we write them? I will know if I have been successful if... I understand what a sample space is. I can write out a sample space using the correct notation. I understand what a compliment is. What is a sample space? In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set. 12

13 Examples Page 1 Ex1.1 Events In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. Sample Space Event 13