Experimental Probability Data Collection L.O. all pupils can gather information all pupils can Main 1: gather information On your paper write down you height (estimate if you do not know) and your handspan : : Jun 19 15:36 Jun 25 08:27 Main 1: gather information Experimental Probability Data Collection L.O. all pupils can gather information all pupils can Jun 19 15:36 o Tally Charts o Two Way Tables o Bar Charts o Scattergraphs (line of best fit, correlation, linear regression) (mean, median, mode, interquartile range) o Cumulative Frequency Diagrams o Boxplots o Tally Charts 1
o Tally Charts Don't forget to label your right hand column 'Frequency' o Tally Charts o Two Way Tables o Two Way Tables 1. How many students participated in the survey? 2. How many students said they "like" snowmobiles? 3. How many of the students "like" snowmobiles, but "do not like" skateboards? 4. How many students said they "do not like" skateboards? Feb 9 11:17 Feb 9 11:17 What do you think a stem and leaf diagram could look like? 2
2 Collect and Organise Data.notebook Here are the marks gained by 30 students in an examination: 63 58 61 52 59 65 69 75 70 54 63 76 81 64 68 59 40 65 74 80 47 53 70 81 68 49 57 61 57 44 3
Worksheet to: a) read off values b) create stem and leaf diagrams c) read off further information What are the arrows indicating? o Bar Charts o Bar Charts 4
o Bar Charts This is a Histogram How is it different to a bar chart? Key Points: NO GAPS area of bar is proportional to frequency frequency density is on the y axis f.d. = freq class width On a histogram, the area of the bar tells us the frequency. On a bar chart, the height of the bar tells us the frequency. On a histogram, the y-axis shows the frequency density On a histogram, the bars are sometimes of equal width. On a Histogram there are no gaps between bars always Bar Chart width 5
Frequency density = frequency class width Frequency density Frequency class width Find the class width for the following intervals: 1) 0 t < 10 2) 10 t < 25 3) 25 t < 45 4) 45 t < 60 5) 60 t < 80 6) 80 t < 90 Jan 17 17:22 Time Frequency Frequency density 0 t < 10 30 30 10 = 3 10 t < 25 30 30 15 = 2 25 t < 45 20 20 20 = 1 45 t < 60 45 45 15 = 3 60 t < 80 80 80 20 = 4 80 t < 90 60 60 10 = 6 Frequency Density 6 5 4 3 2 1 Time Frequency Frequency density 0 t < 10 30 30 10 = 3 10 t < 25 30 30 15 = 2 25 t < 45 20 20 20 = 1 45 t < 60 45 45 15 = 3 60 t < 80 80 80 20 = 4 80 t < 90 60 60 10 = 6 0 10 20 30 40 50 60 70 80 90 Time (minutes) Jan 17 17:22 Dec 17 15:33 How many trees in the wood? Jan 17 17:22 Jan 17 17:22 6
Jan 17 17:22 What do you think of this pie chart? Q1. What is the cost of one if: a) 10 lollipops cost 50p b) 5 apples cost 35p c) 8 packs of crisps cost 64p Q2. There are 40 sweets in 5 packs of polos. How many are there in each pack? Q3. There are 120 matches in 4 boxes. How many are there in each box? Q4. What is the size of the angle of a circle? The table shows some data on the number of children in families. The pie chart shows the same information. 7
How is the size of each segment worked out? What do we know about the size of the angle of a whole circle? 360 o represents 30 families...so how can we work out how many degrees equals one family? 360 30 = 12 o So one family is represented by 12 o. Three families would be represented by 36 o. you will have to group your data into 10cm groups for height and 2cm groups for handspan (line of best fit, correlation, linear regression) To be able to draw scattergraphs, you must be able to plot coordinates y 1. Draw a set of axes in your book from -10 to 10 Where do the coordinates come from in a table like this? 2. Label the x and y axis x 3. Mark the points: (-1,2), (3,4), (5,-6) and (-7,-8) 8
80 60 40 20 0 5 10 15 Jan 27 11:16 Jan 27 11:17 Using the line of best fit, predict how many books would get marked if 3 pints of lager were drunk a line of best fit goes through the middle of the data Jan 27 11:17 Jan 27 11:17 Which line of best fit is correct? Would you describe it as a positive, negative or no correlation? Jan 27 11:17 Jan 27 11:17 9
(mean, median, mode, interquartile range) One will go on the x axis, the other on the y axis. Each point will need to be the same person's height and handspan. (mean, median, mode) (mean, median, mode) In Germany, you only need to really know one type of average (mean/durchschnitt) http://www.youtube.com/watch?v=fuytphvin0i but internationally, you have to know two more averages: median and mode (mean, median, mode) Find the mean, median and mode of these values: 12, 11, 9, 15, 12, 13, 13, 13, 10 (mean, median, mode) 12, 11, 9, 15, 12, 13, 13, 13, 10 Mean Median Mode Add them all up Write them in order Which is the most common? Divide by how many there are Work through to find the middle number What would you do if there was more than one number that occurred 3 times? 10
(range, interquartile range) 12, 11, 9, 15, 12, 13, 13, 13, 10 (range, interquartile range) 12, 11, 9, 15, 12, 13, 13, 13, 10 From the song, can you find the range? What do you think the interquartile range is? Write them in order: 9, 10, 11, 12, 12, 13, 13, 13, 15 Biggest - Smallest 15-9 = range of 6 (range, interquartile range) What do you think the interquartile range is? Find the quarters of the data (range, interquartile range) 9, 10, 11, 12, 12, 13, 13, 13, 15 9, 10, 11, 12, 12, 13, 13, 13, 15 lower quartile median upper quartile lower quartile median upper quartile 13-10.5 = interquartile range of 2.5 (range, interquartile range) Find the median, lower quartile and upper quartile for the following data: (range, interquartile range) Ordering the data, we get 3, 4, 4, 6, 8, 8,10, 10, 11, 12 and 31. 11, 4, 6, 8, 3, 10, 8, 10, 4, 12 and 31. The median is the (11 + 1) 2 = 6 th value. The lower quartile is the (11 + 1) 4 = 3 rd value. The upper quartile is the 3 (11 + 1) 4 = 9 th value. 3, 4, 4, 6, 8, 8, 10, 10, 11, 12, 31 the interquartile range is 11-4 = 7. 11
> mean, median, mode interquartile range > mean, median, mode interquartile range EXTRA PRACTICE!!! find the mean, median, mode and interquartile range for each data set Feb 12 11:50 o Cumulative Frequency Diagrams o Cumulative Frequency Diagrams Do you think we use discrete or continuous data with cumulative frequency curves? Why? o Cumulative Frequency Diagrams o Cumulative Frequency Diagrams Cumulative means... Jan 27 12:04 Jan 27 12:04 12
o Cumulative Frequency Diagrams o Cumulative Frequency Diagrams Jan 27 12:04 Firstly, let's practice o Boxplots o Boxplots o Boxplots o Boxplots Draw a boxplot for this data 13
o Boxplots you have already found the median and interquartile range for each data set so use them to draw a boxplot Feb 27 12:49 14