Statistics. Math grade 8. Ms. Hollenbeck. Mathisfun.com

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1 Statistics Math grade 8 Ms. Hollenbeck Mathisfun.com

2 Statistical surveys Goal: understand the difference between a survey, a study, a census and a poll. Survey: A survey is a data collection (where several questions are asked) involving a sample of a given population (cannot ask everybody so you ask a sample). How to do a survey: 1) Step one: create the questions 2) Step two: ask the questions to a sample group Make sure to choose your sample randomly! Sampling methods Simple random sampling: you choose your sample from the population randomly this way each individual has the same chance of being chosen during the sampling process. Systematic sampling: choosing your samples via a systematic formula that allows for random selections. Choosing a representative sample You must ensure that when choosing a sample of a population for a survey, that the sample has characteristics that closely match the population as a whole. Recognizing possible sources of bias Bias is a favoritism that occurs during the data collection process, which leads to misleading results. For example if you wanted to do a survey on how much holiday shopping people do in Montreal in a year, you shouldn t go out to a mall on boxing day to do this survey because the results are leaning more towards people shopping A LOT! 3) Step three: tally the results (count up the results) Make a frequency table with the data collected after a survey. 4) Step four: present the results (by using a bar graph, pie chart a.k.a circle graph)

3 Study: A study is a survey in which experts are consulted on areas that are being targeted by the survey. Census: A census collects information (where several questions are asked) about every member of a given population. Ex: Statistics Canada sends out a census to each and every home in Canada to collect data about the people who live there. Poll (like a sample survey): A collection of opinions on one subject, taken from either a selected or a random group of people. The numbers are tallied* up. Ex: During an election of a President or a Prime Minister, residents are given the choice between the candidates and they choose one. *Tally The types of variables (data) considered in a survey Data can be qualitative or quantitative. Qualitative data is descriptive information (it describes something). Examples: Your friends' favorite holiday destination The most common given names in your town How people describe the smell of a new perfume Quantitative data, is numerical information (numbers) and there are two kinds: o Discrete quantitative o Continuous quantitative

4 Discrete quantitative variable (data): Discrete quantitative data can only take certain values. It is counted. Example 1: the number of students in a class (you can't have half a student). Example 2: the results of rolling 2 dice: You can only have the values 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 Continuous quantitative variable (data): Continuous Data can take any value (within a range). measured. It is Examples: A person's height: could be any value (within the range of human heights), not just certain fixed heights. The time is takes to get to school, etc. A dog's weight. The length of a leaf. And lots more!

5 Example: Collecting data What do we know about Arrow the Dog? Bar Graph Now using the example about Arrow the dog, lets makes a bar graph with the discrete quantitative variables. Don t forget when making a bar graph to label the axis (x and y) and to give it a title. 7 Quantitative variables about Arrow the dog Number of legs Number of brothers Number of black spots Quantitative variables about Arrow the dog

6 Histograms A histogram is used to represent continuous quantitative data, which is data that is grouped in classes. Example: Height of Orange Trees You measure the height of every tree in the orchard in centimeters (cm) The heights vary from 100 cm to 340 cm You decide to put the results into groups of 50 cm: The 100 to just below 150 cm range [ [ The 150 to just below 200 cm range [ [ etc... So a tree that is 260 cm tall is added to the " " range. The range is also known as the class interval which can be written as [ [ Here is the histogram: You can see (for example) that there are 30 trees from 150 cm to just below 200 cm tall

7 Circle graph (or pie chart) You can represent discrete quantitative data also in a circle graph by using a frequency table. Ex: There are 20 students in a music class that are split up according to the instrument that they play. Here is the frequency table: Instrument Frequency Frequency % Piano 10 50% Violin 5 Cello 2 Flute 1 Other 2 1) Calculate the frequency %. 2) Use cross multiplication in order to determine the degrees for each element in the circle graph. Complete the table below. Example: = Frequency % 360 degrees = 180 degrees INTRUMENTS Piano Violin Cello Flute Other Instrument Degrees Piano 180 Violin Cello Flute Other 10% 5% 10% 25% 50% 3) Practice making the pie chart (Circle graph) with your protractor.

8 Practice question (Histogram, frequency table and tally) Twenty-five students wrote a math test. Here are their results. 60, 75, 55, 87, 70, 70, 97, 63, 90, 86, 45, 77, 59, 48, 71, 63, 73, 91, 71, 89, 70, 63, 57, 88 a) Group the data into six classes with an amplitude (size) of 10 if the lower limit of the 1 st class is 40. Class Tally Frequency % Frequency b) What percentage of students failed the test if 60% is the passing grade? c) In which class are there a. The least number of students? b. The most number of students? d) Make a histogram of the data collected for his math test. Use a ruler. (HINT: use the frequency table) Don t forget to label the axis and give the graph a title.