Statistics Add Ins.notebook. November 22, Add ins

Transcription

1 Add ins We have LOADS of things we need to know for the IGCSE that you haven't learnt as part of the Bavarian Curriculum. We are now going to shoehorn in some of those topics and ideas. Nov 12 11:50 Main 1 : scattergraphs to find correlation Main 1 : scattergraphs to find correlation Describe the correlation by drawing a scatter graph Height (cm) Weight (kg) Define correlation A mutual relationship or connection between two or more things. Interdependence of variable quantities. 2. What are the different ways you can find the correlation? 1

2 Main 1 : scattergraphs to find correlation Main 2: Venn diagrams Main 3: Venn diagrams Blue Red & Blue Red Both Neither Main 2: Venn diagrams Numbers: Both Main 2: Venn diagrams Sometimes you need three sets: Probabilities: Neither Both Neither 2

3 Main 2: Venn diagrams Sometimes you need three sets: Numbers: Probabilities: Main 2: Venn diagrams A maths exam contained only two questions. Problem one was solved by 70% of the pupils. Problem two was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam? In the following year the maths exam contained two percentage problems. This time each problem was solved by 72% of the pupils and every pupil got at least one problem right again. What can you say about the number of pupils in the class? Main 3: intersection and union of sets The INTERSECTION of two sets is the set of elements which are in both sets. It is written with E.g. s = = Main 3: intersection and union of sets Main 3: intersection and union of sets The UNION of two sets is the set of elements which are in either set. Given that A={2,4,6,8,10} and B={1,2,3,4,5} A B = {1,2,3,4,5,6,8,10} the Union It is written with A B = {2,4} the Intersection E.g. s = 3

4 Main 3: intersection and union of sets Main 3: intersection and union of sets Given that A={2,4,6,8,10} and B={1,2,3,4,5} Rules: A B = {1,2,3,4,5,6,8,10} the Union A B = {2,4} the Intersection What is a histogram? The differences between bar charts and histograms What is a histogram? Key Points: NO GAPS area of bar is proportional to frequency frequency density is on the y axis f.d. = freq class width What is a histogram? Histogram On a histogram, the area of the bar tells us the sometimes. On a bar chart, the of the bar tells us the frequency. height width On a histogram, the y-axis shows the On a histogram, the bars are of equal width. On a there are no gaps between bars always Bar Chart frequency density frequency 4

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 Time Frequency Frequency density 0 t < = 3 10 t < = 2 25 t < = 1 45 t < = 3 60 t < = 4 80 t < = 6 Frequency Density Time Frequency Frequency density 0 t < = 3 10 t < = 2 25 t < = 1 45 t < = 3 60 t < = 4 80 t < = Time (minutes) Dec 17 15:33 5

6 Main 5 : mean from continuous data sets just the same method as grouped data Main 5: mean, median and mode of grouped discrete data What is grouped discrete data? The following table shows the number of hours per day of watching TV in a sample of 500 people: a) What is the mean number of TV viewing hours in this group? b) What length of time is most often spent in front of a TV for this group (mode)? c) What is the median number of TV viewing hours? a) What is the mean number of TV viewing hours in this group? a) What is the mean number of TV viewing hours in this group? To get the mean, use this formula: where f is the frequency, x is the midpoint of each interval, and n is the total number of data values. 6

7 a) What is the mean number of TV viewing hours in this group? b) What length of time is most often spent in front of a TV for this group (mode)? To get the mean, use this formula: where f is the frequency, x is the midpoint of each interval, and n is the total number of data values. Looking at the frequency column, we can see that the 4-5 interval occurs most often. So, the mode is the midpoint of that interval, which is 4.5. We could also say that the modal class is 4-5. c) What is the median number of TV viewing hours? The middle data value is between values 250 and 251. Both these data values occur in the 4-5 interval (look at the Cumulative Frequency column). So the median is 4.5, the midpoint of the 4-5 interval. Main 6 : cumulative frequency curve from a table Main 6 : cumulative frequency curve from a table Key Words: cumulative frequency outliers median interquartile range upper quartile lower quartile 7

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