GCSE Maths Week 2 Understand and use statistics and work effectively with a range of charts & graphs

Use the pictures/symbols to find 5 words for today’s lesson 1. + + 2. 19 October 2015 + a 3. + de 4. + to + 5. + GE

COURSE HANDBOOK

Representing data Think about all the different was you know that data can be represented graphically and make a quick sketch on post-its of each one you think of. Make sure you use a separate post-it for each diagram It doesn’t have to be neat or accurate but it does need to be recognisable. Pick one person to stick their diagrams in a row on the wall and write a label describing the diagram underneath.

What have we created?

Data presentation and analysis This is the list from AQA: frequency tables bar charts pie charts pictograms vertical line charts tables line graphs for time series data

histograms cumulative frequency graphs box plots Extra for Higher histograms cumulative frequency graphs box plots

Vocabulary All the vocabulary from the previous slides PLUS http://mathswebsite.com/gcse/aqa/foundation/statistics-probability/v/data-types (Hegarty maths video on other vocabulary i.e. discrete, continuous, qualitative, quantitative etc)

Vocabulary - discrete or continuous? Discrete vs continuous.pptx

A pet shop sells cats. They are available only in 2 types, ginger or white. The shop has 14 male ginger cats. There are 40 cats altogether, and a quarter of them are white. There are 6 female cats that are white. Draw up a table showing the number of each type of cat. What percentage of the cats are white male cats? Suggest a possible reason why the shop has more cats of one type than another.

A pet shop sells cats. They are available only in 2 types, ginger or white. The shop has 14 male ginger cats. There are 40 cats altogether, and a quarter of them are white. There are 6 female cats that are white. Draw up a table showing the number of each type of cat. What percentage of the cats are white male cats? Suggest a possible reason why the shop has more cats of one type than another.

CATS Ginger White Total Male 14 4 18 Female 16 6 22 30 10 40 What sort of table did you draw to organise this data? CATS Ginger White Total Male 14 4 18 Female 16 6 22 30 10 40

Which graph shall I draw? (Mini whiteboards) Choosing and drawing an appropriate diagram is a fairly common exam question and often there is more than one right answer (so don’t worry about what your neighbour writes on their board!)

Data Set 1 Mary recorded the colours of cars in the college car park. Tally Frequency Blue Red Silver Black Green White         5 9 7 4 2 6 Frequency diagram i.e. bar chart, vertical line graph

Data Set 2 The table below shows the percentage of students at a college who achieved grades A* to C (or 9 to 4) in GCSE Mathematics in a five year period. Year 2013 2014 2015 2016 2017 Percentage of students 72 75 79 78 85 Bar chart line graph – over time

Data Set 3 The table below contains information about the type of film 20 students like best. Type of film Comedy Action Romance Drama Scifi Total No. of students 4 5 6 1 20 Pie chart

Pie charts Comedy Action Romance Drama SciFi Total 4 5 6 1 20 Fraction? Percentage? Degrees?

Pie charts Comedy Action Romance Drama SciFi Total 4 5 6 1 20 Fraction? Percentage? Degrees?

Pie charts Comedy Action Romance Drama SciFi Total 4 5 6 1 20 Degrees 72° 90° 108° 18° 360°

Pie charts Comedy Action Romance Drama SciFi Total 4 5 6 1 20 Degrees 72° 90° 108° 18° 360°

Pie charts Comedy Action Romance Drama SciFi Total 4 5 6 1 20 Degrees 72° 90° 108° 18° 360°

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Data Set 4 The speeds, in miles per hour, of cars passing the gates of a primary school in the morning are recorded. Speed 0-5 6-10 11-15 16-20 21-25 26-30 Number of cars 1 6 36 62 26 4 Bar chart with number line on the horizontal axis Why will this chart or graph be different to Data Set 1? Draw a chart for this data deciding on your own scales for each axis.

Data Set 4 The speeds, in miles per hour, of cars passing the gates of a primary school in the morning are recorded. Speed 0-5 6-10 11-15 16-20 21-25 26-30 Number of cars 1 6 36 62 26 4 Bar chart with number line on the horizontal axis Why will this chart or graph be different to Data Set 1? Draw a chart for this data deciding on your own scales for each axis.

Data Set 5 Why will this chart or graph be different to Data Set 4? A librarian notes the number of hours 80 students used the internet over a 7 day period. The information is displayed in the table below. Number of hours Number of students 0  h < 3 5 3  h < 6 7 6  h < 9 18 9  h < 12 20 12  h < 15 25 15  h < 18 Histogram Why will this chart or graph be different to Data Set 4?

Histograms Histograms Lesson.pptx

Data Set 6 An ice-cream van recorded the sales of ice-cream and the temperature over a period of a year. The results are shown in the table below. Outside Temperature (°C) Ice-cream Sales (Hundred £) 8 6 12 9.5 18 16 4 2 10 11 15 13.5 17 14 Scattergraph – we’ll be doing scattergraphs in more detail in week 17.

Why are these graphs misleading? misleadingGraphs TC.ppt (No need to use them all, just pick some)

New content – time series graphs

Interpreting time-series graphs The graph on the next slide shows the maximum temperature in Whitby in January and July each year for a 6 year period (2004 – 2009). Study the graph and answer the questions. AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

What do you think the maximum monthly temperature would have been in March 2006 and October 2008? Temperature (°C) Data taken from http://www.metoffice.gov.uk/pub/data/weather/uk/climate/stationdata/whitbydata.txt March 2006 prediction likely to be about halfway between Jan 2006 and Jul 2006 = 15.1 degrees (see slide 4) Oct 2008 prediction likely to be about halfway between October 2008 and January 2009 = 12.95 (see slide 5) AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

March 2006 – was your prediction correct? Temperature (°C) Data taken from http://www.metoffice.gov.uk/pub/data/weather/uk/climate/stationdata/whitbydata.txt Prediction likely to be round 15.1 (halfway between Jan and Jul) – but the graph is not a straight line so this prediction is not accurate. Actual temperature 7.4 degrees. Difference can be seen by the dotted line, which is the line on the previous slide AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

October 2008– was your prediction correct? Temperature (°C) Data taken from http://www.metoffice.gov.uk/pub/data/weather/uk/climate/stationdata/whitbydata.txt Prediction likely to be round 12.95 (halfway between Jul 2008 and Jan 2009) – but the graph is not a straight line so this prediction is not accurate. However, this is more accurate than the previous slide as it is nearer to the straight line. Actual temperature is 13.2 degrees. AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

Interpreting time-series graphs Time-series graphs can be used to make predictions of future values, although these may not always be accurate. Use the graph on the next slide of the maximum temperature in Whitby to answer the questions. AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

What do you think the maximum monthly temperature would be in January 2010 and July 2010? Data taken from http://www.metoffice.gov.uk/pub/data/weather/uk/climate/stationdata/whitbydata.txt Jan 2011 value – the January values vary from 6 to 9.6 degrees so any estimate in this region is reasonable as there isn’t a particular upward or downward trend– the halfway point of 7.8 degrees might be an appropriate prediction (6.7 was the actual value) Jul 2011 value – the July values vary from 18.8 to 23.4 degrees to any estimate in this region is reasonable as there isn’t a particular upward or downward trend – the halfway point of 21.1 might be an appropriate prediction (18.6 was the actual value) This example shows that predictions can only really be reliable if there is a definite trend to the data. Copyright © 2016 AQA and its licensors. All rights reserved. AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723). Our registered address is AQA, Devas Street, Manchester M15 6EX.

2 Just Maths time series questions

Time Series graph activity In this activity you will generate questions about a graph and describe what the graph is showing. In small groups, spend a couple of minutes studying the graph you have been given. (6 different graphs follow) Devise three questions that could be answered using information from the graph. Swap your questions with another group and answer the questions you have been given, using only information on the graph. Check your answers with the other group.

Amount paid each month (£) over a four year period by an average sized household in a particular town

Topic Test – 20 minutes

Snip in the questions

Website of the week www.corbettmaths.com

Homework Just Maths histogram questions Talk about going over what we’ve done in the lesson. Use Mr Corbett for anything you’re not sure of.