Statistics and Probability 1

This post will cover the first of the posts for Statistics and Probability section for GCSE. It should cover the following objectives :

	•Design and use two-way tables for discrete and grouped data • Design and use two-way tables for discrete and grouped data • Use information provided to complete a twoway table
	• Consider fairness • Understand sample and population • Design a question for a questionnaire • Criticise questions for a questionnaire • Use stratified sampling
	STATISTICS   BASIC CONCEPTS POPULATION The entire population of objects being statistically investigated is called a population. *Examples include the entire set of voters in an election (this population is well defined and finite). An entire batch of components produced at a factory (this population is hypothetical and infinite). SAMPLE A sample is a proportion, usually a relatively small proportion of a population. WHY DO WE NEED DATA ? Statistics is concerned with the properties of the whole population rather than with those of individual objects. Sometimes the entire population is surveyed to determine the characteristics of interest ( as in the population census carried out every ten years), but usually it is only practical to infer population characteristics from information provided by a sample. QUESTIONAIRES AND DATA COLLECTION  A Questionnaire is a type of data collection method. Usually there's a question, and a couple of boxes for choices. We need to know what makes a good questionnaire and a bad one. Example : Susan wants to collect information about the amount of sleep, pupils in her class get.  She designs a questionnaire for this :  (Pretend bullet points are boxes!!) How much sleep do you get ? A lot          Not Much There are two things wrong with this questionnaire : * It's totally rubbish. Why ? 1) The question dosen't refer to how much sleep per .... ? A time frame should be given.. How much sleep per night ? How much sleep per week ? How much sleep per year.... 2) The answers are too ambigious. " A lot of sleep" can be different for different types of people. For me a lot of sleep >10 hours, for some that might mean 14 hours. So secondly, the choices should include some numerical choices. An Improved Questionnaire for the same question would be something like this : How many hours do you sleep per night  ? 5 hours or less More than 5 hours but less than or equal to 7 More than 7 but less than or equal to 8 More than 8 hours but less than or equal to 9 More than 9 hours Though this is much better.. Exercise Question 1) Pick out a flaw from this Questionaire   DATA COLLECTION Tim Wants to Find Out which Soap Opera is the most popular with the pupils in his class. Design a suitable data collection sheet he could use. Soap                                   Tally                                       Frequency Coronation St.                    | | |                                             3 Hollyoaks                           | |                                               2 Eastenders                          | | | |                                           4 Emmerdale                         |                                                 1 Neigbours                          | | |                                              3 *I assume you know how to use tally. We strike through 4 tally marks, for the 5th tally.. and then continue a new tally of 4. *Frequency is just the number of tally  TWO WAY TABLES  Two Way Tables are another way of representing data, where they are two variables, and some choices for those variables. In a Two Way Table, the far right handside column will be TOTALS, as will be the bottom most row. The far right, and bottom box/cell contains the Total for all the columns and the Total for all the rows. a = 10, b = 9, c= 15, d = 24 and e = 28. To Check Working Out Look Below This example above is a Two-Way Table, where the totals' at the bottom are the total of all the boxes above them, and the totals' on the right hand side, are the total of all the boxes to the left of them Q) Work out the Missing Variables a,b,c,d and e. Well 13 + a + b = 32 So there's two unknown's so it's hard to work out. b + 19 = 28, so b = 9 13 + a + 9 = 32 so a = 10 10 + d = 34, so d = 24 c + 24 + 19 =58 so c = 15 13 + 15 = e e = 28  DESIGNING A GOOD QUESTIONNAIRE Tony wants to open a new restaurent. He wants to know what type of food people like. Design a suitable questionnaire he could use to find out what type of food people like ? A good answer is made up of an unbiased question (not too much emphasis on one side of the coin, and not leading the person answering to make a preferred answer)... and good choices for the answers ( a range). Example : What type of food do you like eating? Indian Chinese Italian Other Example Question 1 ) Mr Nicholson wants to find out what pupils think of his lessons. His questionnaire is as follows : What do you think of my lessons? Excellent Very Good Good a) What is wrong with the question ? *There is no choice for negative answers (bad, very bad) Exercise Question 1) How much time do you spend on Homework ? A lot Not much a) What is wrong with the questionnaire ? b) Design a better questionnaire Exericse Question 2) Sarah wants to find out what pupils think of the School Canteen. She plans to stand outside the Canteen at 12.30pm, and ask the Year 7 pupils to fill a questionnaire. a) Why is this biased ? b) Describe a way to make it less biased ? STRATIFIED SAMPLING Stratified Sampling is a type of sampling method from a population. When the number of people in certain sub groups of the population vary, a stratified sample may be used. First the Sample is of 100 students, notice how there are different people in most of the different groups (boys different to girls, yr 7 different to yr 9, etc.) First we get the sample percentage, we find this out  by the formula : Sample Size / Population Size. In this case the Sample Size is 100, the Population Size is the total of all the people so (70 +30 + 100 + 100 + 300 + 400 = 1000) 100/1000 = 0.1 Now we multiply this decimal by the number of people in each category (stratum size), to find out how many people of the category will be included in the sample : Yr 7 Boys = 70 * 0.1 = 7 Yr 7 Girls = 30 * 0.1 = 3 Yr 8 Boys = 100 * 0.1 = 10 Yr 8 Girls = 100 * 0.1 = 10 Yr 9 Boys = 300 * 0.1 = 30 Yr 9 Girls = 400 * 0.1 = 40  Exercise Question 3)