GCSE Session 24 Discrete and Continuous Data Statistical

GCSE Session 24 - Discrete and Continuous Data, Statistical Problem Solving GCSE MATHS

Higher Only � For non right angled triangles, the Sine rule can be used. (chapter 34) Ex 34. 4 Q 1 (5 min)

� To use the sine rule to find an angle, you need the length of the side opposite, and the length of a side opposite a known angle. � To use the cosine rule to find a side of a triangle, you need two sides and the angle between them.

� The cosine rule Ex 34. 6 Q 1 Ex 34. 9 10 minutes

Data � Primary – data you have collected yourself, obtained form experiments, surveys, investigations or questionnaires � Secondary – data taken from nay other source; statistics, trends, research, other people’s investigations.

� Page 388 read examples and discuss Ex 35. 1 (3 minutes)

Tally Charts � Basic tally chart (frequency distribution) � Grouped frequency distribution with class intervals (using in equalities)

Data collection card/ database � Multiple information about one subject can be stored on a data collection card � Multiple information about more than one item can be collected in a basic database (see example page 390) � These can be used to create charts as on the previous slide, where only 1 variable is used. � Ex 35. 2 – 10 minutes

The Hypothesis � The hypothesis is a statement that you are trying to test. � When we construct a questionnaire, keep in mind that the questions should assist us in proving or disproving the validity of the hypothesis.

Questionnaires � Read page 392 � If you provide multi choice questions, you must cover all possible answers � Eg What is your favourite colour? � Black � Red � Green

� For our purpose we want the be able to analyse the responses numerically, so avoid qualitative responses, or use multi choice options � Eg instead of saying ‘describe yourself’ � Say ‘ which of the following statements best describes you’ � Ex 35. 3

Two way tables � There is an example of a simple 2 way table on page 393. � They sort our information into different categories, allowing form more analysis based on those categories. � We may need to apply our knowledge of fractions, decimals and percentages to draw out useful statistics from these tables. � See next slide then attempt Ex 35. 4

Two way tables � Below is an example of a two-way table showing the number of boys and girls in a 6 th form college: Lower 6 th Upper 6 th Boys 140 100 Girls 120 140 We can find out lots of information from this table, for example: � There are 260 girls in the college (120 + 140) � 5/12 of the boys are in U 6 (100 out of 240) � 48% of the pupils are boys (240/500 × 100)% � If a girl is chosen at random, the probability that she is in class L 6 is 6/13 (there are 260 girls, and 120 of them are in L 6, so 120/260 or 6/13)

Sampling � When we want to find results than can be applied to a large population, it is impossible to ask every single person. To test the hypothesis: � ‘Dogs are the most popular pet in Britain’ Would you ask every single person in Britain? Of course not, you need to find a suitable sample that represents the diversity in the whole of Britain.

� Simple random sample – everyone has an equal chance of being selected (must be random) � Systematic random sample – people are selected based on a particular rule � Stratified random sampling – the original group is divide into categories, but these categories are samples in proportion to the original group. � Ex 35. 5, discuss the ‘give a reason’ questions with a partner and work the calculation questions together.

Revision � Revise � Don’t Number, Algebra and Geometry. waste the 2 weeks off at Easter. � There are only 6 teaching weeks after Easter up to half term, (one may be used as a mock) then the exams are immediately after half term. � Your best chance of achieving the grade you want is to revise and prepare for the exams.