Solution:

Statistics

Subject knowledge sessions  Date Time     Topic 04-01-17 9.00-12.00 AM Statistics PTSA Scott Yalden 11-01-17 Probability Richard Whitehouse 18-01-18 Problem Solving and Numerical Methods Donna Roughton 25-01-18 Higher Ability KS4 Tavistock 01-02-18 Bridging unit - introduction to A Level

9-1 GCSE Mathematics - Statistics Content

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Year 6

Match the keyword with the definition. Categorical Data Data that is measured and can take a whole range of values Bivariate Data Data is counted i.e. can only take certain values Discrete Data Non – numerical data Continuous Data Data you have collected yourself e.g. by experiment or survey. Primary Data Data that has two variables Secondary Data Numerical data (numbers) Quantitative Data Data obtained from other sources e.g. internet or newspaper Qualitative Data that is grouped into categories

Solutions Categorical Data Data that is grouped into categories Bivariate Data Data that has two variables Discrete Data Data is counted i.e. can only take certain values Continuous Data Data that is measured and can take a whole range of values Primary Data Data you have collected yourself e.g. by experiment or survey Secondary Data Data obtained from other sources e.g. internet or newspaper Quantitative Data Numerical data (numbers) Qualitative Non – numerical data

Hypotheses A good hypothesis is a statement not a question.

Types of sampling

Processing and representing data

Histograms

The area of the histogram represents area. The histogram shows the times a sample of students spent on the internet one evening. (a) Copy and complete the frequency table, (b) Estimate how many students spent longer than 50 minutes on the internet. Time, t, minutes 0 ≤ t < 20 20 ≤ t < 30 30 ≤ t < 35 35 ≤ t < 45 45 ≤ t < 60 Frequency 0.1 x 20 = 2 0.8 x 10 = 8 2.8 x 5 = 14 1.5 x 10 = 15 0.4 x 15 = 6 0.4 0.8 1.2 1.6 2.0 Frequency Density 2.4 2.8 50 Minutes or more The area of the histogram represents area. Area 50 ≤ t < 60 = 0.4 x 10 = 4 4 students spent longer than 50 minutes on the internet. 10 20 30 40 50 60 Time (Minutes)

Draw a histogram to represent this data.

Quartiles  

Box Plots A box plot is a way of illustrating key information about a set of data They are also very useful for comparing the distribution of two sets of data (e.g. boys vs girls)

Box Plots To draw a box plot, you need FIVE pieces of information: The minimum value The lower quartile The median The upper quartile The maximum value

Box Plots

Box Plots Below are the midday temperatures for Ringwood over the past 11 days (in oC). 20, 22, 16, 17, 16, 18, 20, 18, 16, 21, 18 Below are the midday temperatures for Glasgow over the past 11 days (in oC). 17, 20, 20, 17, 16, 14, 13, 19, 21, 17, 18 Draw box plots for the data and write some comments on what they tell you about the temperatures in Ringwood and Glasgow over the past 11 days.

Cumulative Frequency and Box Plots The table below shows the ages that men from two professions spotted their first grey hair. Teachers Doctors Age, y, years Frequency Cumulative Frequency 20 < y ≤ 25 5 25 < y ≤ 30 15 14 30 < y ≤ 35 12 19 35 < y ≤ 40 6 40 < y ≤ 45 2 1 5 20 14 32 33 38 39 40 40 Calculate the cumulative frequencies Draw cumulative frequency curves on the same axes Use your cumulative frequency curves to draw box plots to compare the data Write sentences to explain what your box plots show you.

Median = 40 ÷ 2 = 20th value Median (T) = 30 years Median (D) = 32 years LQ = ¼ x 40 = 10th value LQ (T) = 27 years LQ (D) = 29 years UQ = ¾ x 40 = 30th value UQ (T & D) = 34 years 40 Cumulative Frequency 35 30 25 Teachers Doctors 20 15 10 5 Age 20 25 30 35 40 45 50

40 Cumulative Frequency 35 30 Teachers 25 Doctors 20 On average, teachers go grey at a younger age as their median is lower However, doctors go grey at a more similar age as their range and interquartile range is smaller. 15 10 5 20 25 30 35 40 45 50 Teachers Doctors

Box plot match Here are six cumulative frequency graphs and six box plots of the same data. Can you match them up?

Average number of hours TV watched per week Scatter graphs Average number of hours TV watched per week IQ 42 89 14 103 22 94 16 91 2 116 26 3 15 106 95 8 10 115 100 27 6 102 90 9 88

Other types of chart

References: Mathematics programmes of study: key stages 1 and 2 National curriculum in England NRICH M, M and M Histograms