Subject Knowledge Enhancement Surrey Plus Maths Hub Subject Knowledge Enhancement Data collection, averages and graphs Henry Stevenson, Weydon School 5 12 7 13 ? Mean = 10

Purpose: Session 1 - Thursday 14th May 2015 Statistical Calculations To be familiar with the National Curriculum Programme of Study To develop subject knowledge of statistical calculations To develop a range of classroom activities and resources

KS3 Programme of Study § Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

KS4 Programme of Study § infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling § interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data, including box plots appropriate measures of central tendency (including modal class) and spread including quartiles and inter-quartile range § apply statistics to describe a population

Data Collection Time Hair colour Number of siblings Height Types of data Tallying Grouping data Sampling Questionnaires Surveys Dress Size Football Team GCSE Grade Weight Test score Age Speed Shoe Size

Ed Milliband would destroy the British economy. How often do you go swimming? Regularly Quite often Not very often Sometimes Never Ed Milliband would destroy the British economy. Agree Disagree Height: 120-140 140-160 160-180 180-200 Weight: kg How much homework do you do? 0 1 2 3 4+

Is there a 'right' and a 'wrong' way to group data? Tomato Plants 67 10 59 66 24 49 28 62 18 42 63 17 74 68 26 35 23 44 80 61 56 76 38 15 6 47 54 41 34 5 52 77 22 72 40 31 43 79 Is there a 'right' and a 'wrong' way to group data?

Football manager You have to pick one striker in your team for the cup final. Who will you pick and why? Gianlucca Vialli 0 0 3 3 1 3 0 2 Gianfranco Zola 2 2 1 2 1 2 1 1 Tore Andre Flo 1 4 0 0 0 4 3 0

Averages and Spread Concerns: Weaker students can't remember them Stronger students get bored

Mean is 18, median is 12, range is 17 What was the question? Write down 5 numbers which : Mean is 18 ... and another one... Mean is 18, range is 6 Mean is 18, median is 12 Mean is 18, median is 12, range is 17 Median is 15, mode is 20, range is 10, mean is ?

What questions would you ask? Pocket Money Pocket Money Frequency £0 2 £1 1 £2 £3 4 £4 5 £5 Pocket Money Frequency £0 £1 6 £2 8 £3 7 £4 9 £5 Pocket Money Frequency £0 12 £1 6 £2 £3 24 £4 30 £5 What questions would you ask?

Averages from grouped data What do you think are the most common misconceptions?

Is the average salary really £50,000? Weighted means Is the average salary really £50,000? Director £80,000 1 Supervisor £50,000 5 Attendant £20,000 14 Average salary French exam Biology Score Speaking 45% 1/6 Listening 90% 3/6 Writing 68% 2/6 Paper 1 38/50 40% Paper 2 41/50 Controlled Assessment 29/50 20%

Boys 18 31 32 33 34 35 45 Girls 20 22 24 25 28 29 38 40 Puzzle Times Compare the distribution of the boy's times to the girl's times.