# Reading charts and graphs Interpreting Data Bridging the gap to.

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Reading charts and graphs Interpreting Data Bridging the gap to

Welcome to all learners! Click to read on … Do You …Do You … - know how to read bar charts?- know how to read bar charts? You need a slide show that is … - Clear! - easy to follow - learner-friendly: 1 step at a time - for beginners AND revisers! This slide show will …This slide show will … - Give you a user-friendly way to read bar charts!- Give you a user-friendly way to read bar charts!

Reading bar charts How to use this resource You can control how fast or slow you go, using: FORWARD: OR OR Enter OR Left-hand mouse BACK: OR OR Back Space TO START SLIDESHOW: F5 OR Slide Show > View Show TO END SLIDESHOW: Escape

Reading bar charts Interpreting Data If you want to get the BIG PICTURE first about Data Handling … … why not try the introductory slide show: Introduction to Data Handling ! at www.bgfl.org/mathsbooster (School Booster)

Reading bar charts Recap: 3 Steps in Data Handling 1. Collect the data Get the information you need 1. Collect the data Get the information you need H e i gh t N u m b e r l e ss t han 1 50 c m h i gh 9 l e ss t han 1 50 c m h i gh 2 0 m o r e t han 2 00 c m h i gh 1 3 0 6Ks bedtimes: 8:30pm, 8:00 pm, 7:45 pm, 9:30 pm, 7:00 pm, 10:00 pm, 7:20 pm, 8:15pm, 7:29 pm, 11:45 pm, 8:50 pm, 8:15 pm,9:00 pm, 7:18 pm, 9:25 pm, 10:30 pm, 8:18 pm 3.Interpret the data Explain it! … Say what it means! Draw some conclusions! 3.Interpret the data Explain it! … Say what it means! Draw some conclusions!

Reading bar charts Recap: 3 Steps in Data Handling Step 1. Collect the data Step 2. Organise & display the data Step 3. Interpret the data Height Number less than 150cm high 9 less than 150cm high 20 more than 200cm high 1 30 6Ks bedtimes: 8:30pm, 8:00 pm, 7:45 pm, 9:30 pm, 7:00 pm, 10:00 pm, 7:20 pm, 8:15pm, 7:29 pm, 11:45 pm, 8:50 pm, 8:15pm, 9:00 pm, 7:18 pm, 9:25 pm, 10:30 pm, 8:18 pm

Reading bar charts Recap: The Traffic Lights Method RED: STOP AND LOOK! … AT THETitle Axes Numbers and scale AMBER: GET READY TO READ! Turn each bar into English so that the graph makes sense before you start … Always Make Bars Easy Reading GREEN: GO AND READ THE GRAPH! SAY WHAT YOU SEE - The tallest bar? Shortest bar? Differences between the bars?

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the title? 10 9 8 7 6 5 4 3 2 1 0 Number of pupils What does the title say the graph is about? 6Ks Bedtimes Bedtime 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Example 1

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the x-axis? 10 9 8 7 6 5 4 3 2 1 0 Number of pupils What does the x-axis show? 6Ks Bedtimes 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Bedtime Question What if a pupil says that they go to 8pm? Should their data go into the 1 st or 2 nd bar? Answer It doesnt matter – as long as you decide the same rule for all results! In this survey, borderline results were put in the higher bar. Example 1

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the y-axis? What does the y-axis show? 10 9 8 7 6 5 4 3 2 1 0 Number of pupils 6Ks Bedtimes 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Bedtime Example 1

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale What y numbers do we have? What x numbers do we have? 10 9 8 7 6 5 4 3 2 1 0 Number of pupils 6Ks Bedtimes 5 bedtime slots from 7pm to Midnight. 1 -10: easy numbers! What scale? 1 hour bedtime slots. What scale? The y-axis goes up in 1s - so its very easy to read! 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Bedtime Example 1

Reading bar charts AMBER: GET READY TO READ! Always Make Bars Easy Reading Reading bar charts AMBER: GET READY TO READ! Always Make Bars Easy Reading 10 9 8 7 6 5 4 3 2 1 0 Translate each bar into a sentence! Click here for Translator: Maths to English Number of pupils 6Ks Bedtimes Bedtime 1 pupil after 11 10 pupils go to bed between 8pm and 9pm. 8 pupils go to bed between 9pm and 10pm. 9 pupils go to bed between 7pm and 8pm. 2 pupils 10-11pm. 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Example 1

6Ks Bedtimes The shortest bar means …? The tallest bar means …? 10 9 8 7 6 5 4 3 2 1 0 Number of pupils Bedtime Reading bar charts GREEN: GO AND READ! – the tallest and shortest 10 pupils go to bed between 8pm and 9pm. 1 pupil after 11 SHORTEST BAR 11pm - Midnight is the least popular bedtime. TALLEST BAR 8pm - 9pm is the most popular bedtime. 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Mode Most popular (1 kind of average) Example 1

7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Reading bar charts GREEN: GO AND READ! 6 ways to say what you see – about the mode Bedtime 10 9 8 7 6 5 4 3 2 1 0 Number of pupils 10 pupils go to bed between 8pm and 9pm. OR … The modal bedtime is 8pm to 9pm. OR … The most popular bedtime is 8pm to 9pm. OR … Most Y6K pupils go to bed between 8pm to 9pm. OR … The most common bedtime is 8pm to 9pm. OR … The most frequent bedtime is 8pm to 9pm. OR … The bedtime with the highest frequency is 8pm to 9pm. Example 1

6 more pupils go to bed 9pm - 10pm than those who go at 10pm - 11pm. 8 = 2 + 6 6 more pupils go to bed 9pm - 10pm than those who go at 10pm - 11pm. 8 = 2 + 6 9 fewer pupils go to bed 11pm - Midnight than those who go between 8pm - 9pm. 10 – 9 = 1 9 fewer pupils go to bed 11pm - Midnight than those who go between 8pm - 9pm. 10 – 9 = 1 5 times as many pupils go to bed 8pm - 9pm as those who retire 10pm - 11pm. 10 = 5 x 2 5 times as many pupils go to bed 8pm - 9pm as those who retire 10pm - 11pm. 10 = 5 x 2 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Reading bar charts GREEN: GO AND READ! – compare the bars 10 9 8 7 6 5 4 3 2 1 0 Number of pupils 6Ks Bedtimes Bedtime Half as many pupils go to bed 11pm - Midnight as those who go between 10pm – 11pm. 1 = 1/2 of 2 Half as many pupils go to bed 11pm - Midnight as those who go between 10pm – 11pm. 1 = 1/2 of 2 Can you find some other things to say about this graph? You might want to use: more than + fewer than - times x of ÷ Can you find some other things to say about this graph? You might want to use: more than + fewer than - times x of ÷ Example 1

Reading bar charts GREEN: GO AND READ! – the total of the bars 10 9 8 7 6 5 4 3 2 1 0 Number of pupils The total of all bars means …? TOTAL OF ALL BARS = Total number of pupils … 9 10 8 2 + 1. Total = ? TOTAL OF ALL BARS = Total number of pupils … 9 10 8 2 + 1. Total = ? Total = 30 pupils 6Ks Bedtimes Bedtime 1 pupil 10 pupils 8 pupils 9 pupils 2 pupils 7pm 8pm 9pm 10pm 11pm. to to to to to 8pm 9pm 10pm 11pm Midnight Example 1

Can you tell anything from this graph shape? More pupils go to bed earlier rather than later! What about the shape of this graph? Reading bar charts GREEN: GO AND READ! - the graph shape 6Ks Bedtimes6Ls Bedtimes6Ms Bedtimes … and this one? Roughly the same number of pupils go to bed earlier and later More pupils go to bed later rather than earlier! Example 1

Reading bar charts Example 2 6K have a fantastic football team! Their captain collected data on how many goals the 6K team scored in each match…

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the title? 10 9 8 7 6 5 4 3 2 1 0 Frequency What does the title say the graph is about? 6Ks goal score per game Number of goals 1 2 3 4 5 Example 2

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the x-axis? 10 9 8 7 6 5 4 3 2 1 0 Frequency What does the x-axis show? 6Ks goal score per game 1 2 3 4 5 Number of goals Example 2

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the y-axis? What does the y-axis show? 10 9 8 7 6 5 4 3 2 1 0 Frequency 6Ks goal score per game 1 2 3 4 5 Number of goals Example 2

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale What y numbers do we have? What x numbers do we have? 10 9 8 7 6 5 4 3 2 1 0 Frequency 6Ks goal score per game 5 goal scores 1 - 5 1 -10: easy numbers! What scale? Goes up in 1s What scale? The y-axis goes up in 1s - so its very easy to read! 1 2 3 4 5 Number of goals Example 2

Reading bar charts AMBER: GET READY TO READ! Always Make Bars Easy Reading Reading bar charts AMBER: GET READY TO READ! Always Make Bars Easy Reading 10 9 8 7 6 5 4 3 2 1 0 Translate each bar into a sentence! Click here for Translator: Maths to English Frequency 6Ks goal score per game Number of goals 1 5-goal match There are 10 2-goal matches There are 8 3-goal matches There are 9 1-goal matches 2 4-goal matches 1 2 3 4 5 Example 2

6Ks goal score per game The shortest bar means …? The tallest bar means …? 10 9 8 7 6 5 4 3 2 1 0 Frequency Number of goals Reading bar charts GREEN: GO AND READ! – the tallest and shortest There are 10 2-goal matches 1 5-goal match SHORTEST BAR 5 goals is the least popular goal score TALLEST BAR 2 goals is the most popular goal score 1 2 3 4 5 Mode Most popular (1 kind of average) Example 2

1 2 3 4 5 Reading bar charts GREEN: GO AND READ! 6 ways to say what you see – about the mode Number of goals 10 9 8 7 6 5 4 3 2 1 0 Frequency There are 10 2-goal matches OR … The modal goal score is 2. OR … The most popular goal score is 2. OR … More matches score 2 goals than any other score. OR … The most common goal score is 2. OR … The most frequent goal score is 2. OR … The goal score with the highest frequency is 2 goals. Example 2

There are 6 more 3- goal matches than there are 4-goal matches. 8 = 2 + 6 There are 6 more 3- goal matches than there are 4-goal matches. 8 = 2 + 6 There are 9 fewer 5- goal matches than there are matches 2- goal matches 10 – 9 = 1 There are 9 fewer 5- goal matches than there are matches 2- goal matches 10 – 9 = 1 1 2 3 4 5 Reading bar charts GREEN: GO AND READ! – compare the bars 10 9 8 7 6 5 4 3 2 1 0 Frequency 6Ks goal score per game Number of goals There are 5 times as many 2-goal matches as there are 4-goal matches. 10 = 5 x 2 There are 5 times as many 2-goal matches as there are 4-goal matches. 10 = 5 x 2 Half as many matches scored 5 goals as matches which scored 4 goals. 1 = 1/2 of 2 Half as many matches scored 5 goals as matches which scored 4 goals. 1 = 1/2 of 2 Example 2 Can you find some other things to say about this graph? You might want to use: more than + fewer than - times x of ÷ Can you find some other things to say about this graph? You might want to use: more than + fewer than - times x of ÷

Reading bar charts GREEN: GO AND READ! – the total of the bars 10 9 8 7 6 5 4 3 2 1 0 Frequency The total of all bars means …? TOTAL OF ALL BARS = Total number of matches … 9 10 8 2 + 1. Total = ? TOTAL OF ALL BARS = Total number of matches … 9 10 8 2 + 1. Total = ? Total = 30 matches 6Ks goal score per game Number of goals 1 match 10 matches 8 matches 9 matches 2 matches 1 2 3 4 5 Example 2

Can you tell anything from this graph shape? 6K played more low- scoring matches than high-scoring matches! What about the shape of this graph? Reading bar charts GREEN: GO AND READ! - the graph shape Which class has the best football team? 6Ks goal score per game 6Ls goal score per game 6Ms goal score per game … and this one? 6L played roughly an equal number of low-scoring and high scoring matches. 6M played more high- scoring matches than low-scoring matches! Example 2

Reading bar charts Example 3 Mr Cruncher is going to teach Year 6 (6K and 6L) about bar charts (yey!) He decides to test them first to see what they already know …

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the title? 20 18 16 14 12 10 8 6 4 2 0 Number of pupils What does the title say the graph is about? Y6 Test Results Marks out of 100 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Example 3

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the x-axis? 20 18 16 14 12 10 8 6 4 2 0 Number of pupils What does the x-axis show? Y6 Test Results 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Marks out of 100 Example 3

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Where is the y-axis? What does the y-axis show? 20 18 16 14 12 10 8 6 4 2 0 Number of pupils Y6 Test Results 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Marks out of 100 Example 3

Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale Reading bar charts RED: STOP AND LOOK AT: Title Axes Numbers and scale What y numbers do we have? What x numbers do we have? 20 18 16 14 12 10 8 6 4 2 0 Number of pupils Y6 Test Results 5 grades covering marks from 1 to 1 – 100. 1 – 20, quite easy numbers What scale? 20 marks per grade. What scale? The y-axis goes up in 2s - A little harder to read (so take care!) 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Marks out of 100 Example 3

Reading bar charts AMBER: GET READY TO READ! Always Make Bars Easy Reading Reading bar charts AMBER: GET READY TO READ! Always Make Bars Easy Reading 20 18 16 14 12 10 8 6 4 2 0 Translate each bar into a sentence! Click here for Translator: Maths to English Number of pupils Y6 Test Results Marks out of 100 2 pupils scored A 20 pupils scored a D 16 pupils scored a C. 18 pupils scored an E 4 pupils scored a B 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Example 3

Y6 Test Results The shortest bar means …? The tallest bar means …? 20 18 16 14 12 10 8 6 4 2 0 Number of pupils Marks out of 100 Reading bar charts GREEN: GO AND READ! – the tallest and shortest 20 pupils scored a D 2 pupils scored A SHORTEST BAR Grade A is the least popular test result. TALLEST BAR Grade D is the most popular test result. 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Mode Most popular (1 kind of average) Example 3

1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Reading bar charts GREEN: GO AND READ! 6 ways to say what you see – about the mode Marks out of 100 20 18 16 14 12 10 8 6 4 2 0 Number of pupils 20 pupils scored a D OR … The modal test result is a D! OR … The most popular test result is a D. OR … Most Y6K pupils scored a D. OR … The most common test result is a D. OR … The most frequent test result is a D. OR … The test result with the highest frequency is a D. Example 3

12 more pupils scored a C than a B. 16 = 4 + 12 12 more pupils scored a C than a B. 16 = 4 + 12 18 fewer pupils scored an A than a D. 20 – 18 = 2 18 fewer pupils scored an A than a D. 20 – 18 = 2 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Reading bar charts GREEN: GO AND READ! – compare the bars 20 18 16 14 12 10 8 6 4 2 0 Number of pupils Y6 Test Results Marks out of 100 Example 3 5 times as many pupils scored a D as a B. 20 = 5 x 4 5 times as many pupils scored a D as a B. 20 = 5 x 4 Half as many pupils scored an A as a B. 2 = 1/2 of 4 Half as many pupils scored an A as a B. 2 = 1/2 of 4 Can you find some other things to say about this graph? You might want to use: more than + fewer than - times x of ÷ Can you find some other things to say about this graph? You might want to use: more than + fewer than - times x of ÷

Reading bar charts GREEN: GO AND READ! – the total of the bars 20 18 16 14 12 10 8 6 4 2 0 Number of pupils The total of all bars means …? TOTAL OF ALL BARS = Total number of pupils 18 20 16 4 + 2. Total = ? TOTAL OF ALL BARS = Total number of pupils 18 20 16 4 + 2. Total = ? Total = 60 pupils Y6 Test Results Marks out of 100 2 pupil 20 pupils 16 pupils 18 pupils 4 pupils 1 - 20 21 - 40 41 – 60 61 – 80 81 – 100 E D C B A Example 3

Reading bar charts The next step! Did you know that reading bar charts is one of the trickiest brain-teasing tightropes in maths you can try! Now that youve tackled this topic, why not try some of the other maths boosters? You can check out some of the other slide shows at: www.bgfl.org/mathsbooster (School Booster)