Dŵr y Felin Comprehensive School. Data Handling Methodology Booklet

Transcription

1 Dŵr y Felin Comprehensive School Data Handling Methodology Booklet

2 Data Handling When representing data the following steps are followed Step 1 Step 2 Step 3 Step 4 Conducting a survey to obtain the data Data Collation Representing Data Conclusions In mathematics lessons pupils are taught to follow the steps, but omitting some steps depending on the question. In the following booklet key teaching points have been highlighted for each step including any common misconceptions. Key Teaching Point. Before starting to use graphs/tables or charts it is important that pupils understand the difference between continuous and discrete data. This will have an impact on how they set out their questionnaire and which graph they use. Discrete Data. Discrete data is data resulting from counting separate items or events, e.g. number of people, colour of cars, favourite food etc. Continuous Data Continuous data is data resulting from measurement, e.g. length, temperature, weight etc. It is possible for continuous data to take any value between two values. References to discrete and continuous data will be made throughout this booklet. Throughout these topics the following skills are inherent Strand Developing Numerical reasoning Element Identify processes and connections Transfer mathematical skills across the curriculum in a variety of contexts and everyday situations Choose an appropriate mental or written strategy and know when it is appropriate to use a calculator Identify, measure obtain required information to complete the task Select appropriate mathematics and techniques to use Strand Developing Numerical reasoning Element Represent and communicate Explain results and procedures precisely using appropriate mathematical language Select and construct appropriate charts, diagrams and graphs with suitable scales

3 Conducting a Survey. Strand Using Data Skills Element Collect and Record Data Collect own data for a survey e.g through designing a questionnaire (Yr 7) Plan how to collect data to test hypotheses (Yr 8) Sometimes pupils have to obtain their own information to answer problems. This is usually done using a questionnaire. Tips for designing a good questionnaire. Questions should be short, clear and easy to understand. People have to know what you mean. Questions should not be biased. Don t ask leading questions. Don t ask upsetting or embarrassing questions. People will not answer honestly. Questions should be relevant to the survey. Give choices for answers, but remember to include a catch all. This makes it easier to represent your data. Preparing to draw any table, chart or graph. It is important to stress to the pupils the importance of using the correct equipment to draw any table, chart or graph. As a Maths department we encourage pupils to have their own equipment. Equipment List Sharp pencil Ruler Rubber Square or graph paper (bar, line or scatter graphs) A protractor (pie chart) A compass (pie chart)

4 Data Collation. Strand Using Data Skills Element Collect and Record Data Construct frequency tables for sets of data, grouped where appropriate, in equal class intervals (groups given to learners) (Yr 7) Once the pupils have collected the data (or data is given to them) they are taught to produce a tally chart. Once the information is correctly placed into a tally chart then pupils can decide which graph/chart they can use to display the information. (It should be noted that the internet can be used as a source of data collection). Example of a Frequency Diagram (Tally Chart). Discrete Data. Sam decides to record the colour of the cars passing his house in one hour. Below are the results. B Blue, R Red, S Silver, Bl Black, O Other B R R S S Bl O O O B B R R S S S Bl Bl S S S S O O B S S Bl Bl Bl R R R R O B Colour of Car Tally Frequency Blue //// 5 Black //// / 6 Red //// /// 8 Silver //// //// / 11 Other //// / 6 Total 36 Key Features The tally chart must have a frequency column The tallies must be drawn in groups of 5 (////) Pupils must check the number of values matches with the total frequency. Common Misconceptions Missing out some of the data Incorrectly counting up the tally marks. Once an appropriate tally chart has been drawn then the pupil can decide/be guided towards which graph/chart is most appropriate to use.

5 Representing data in various graphs and diagrams Strand Using Data Skills Element Present and analyse data Construct a wide range of graphs and diagrams to represent the data and reflect the importance of scale (Yr 7) Choosing a Suitable Scale. Before the pupils begin to draw any graphs that require a scale you will have to discuss scales in detail. Pupils often find scale confusing to understand and interpret. In mathematics lessons a significant amount of time is spent explaining how to use appropriate scales. It is therefore important that time is given to ensure that pupils understand the scale that they are going to use before starting to draw any graph. Steps to be followed to draw suitable scales. 1. Look at the largest number that has to be plotted on each axis then draw the scale so that it goes just beyond your biggest number. 2. Make sure that the pupils are able to work out how much each small square is worth. 3. The scale should go up by the same amount each time. 4. Write the numbers on the lines and not in the spaces The zig zags mean that we have omitted 0 to 40 and 0 to 50

6 Drawing a Bar Chart. Strand Using Data Skills Element Present and analyse data Construct a wide range of graphs and diagrams to represent the data and reflect the importance of scale (Yr 7) Interpret diagrams and graphs (Yr 7) Construct a wide range of graphs and diagrams to represent discrete and continuous data (Yr 8) Bar charts are good for displaying simple data easily. They are most commonly used to display numerical discrete data e.g. shoe size or non numerical discrete data e.g. hair colour and is therefore important that spaces are left between the bars. Key Features. All graphs must have a title All graphs must be drawn on squared or graph paper (depending on ability) Bars must be equal width and have equal spaces in between them Labels must be placed on the horizontal and vertical axes An appropriate scale must be used on the vertical axis. Common Misconceptions No title or labels Bars not being the same width No space between the bars Inappropriate scales being used. Example of a discrete data bar chart. The bar chart below shows information about the score of a certain game. Bar chart to show the score in a game Score is discrete data since you can only score 1, 2, 3 etc and not 1.2 or 2.6 etc.

7 Bar charts can also be used to display continuous data i.e. data that can take any value in a certain range e.g. how many minutes does it take to travel to school. This bar chart is drawn with bars touching Example of a continuous data bar chart. The graph below shows information about the handspans of pupils in a year 7 class. Bar chart to show handspans of a year 7 class Handspans are continuous data since a measurements are not exact they can be 14.4cm or 15.75cm etc.

8 Drawing a Pictogram Pictograms are used for discrete data. A pictogram is a visual way of displaying data and is usually one of the easiest types of graph for lower ability pupils to construct and use. Key Features Pictures represent numerical data. All pictograms must have a title. Pictures must be equal size. A picture can represent any number the number that the picture represents is shown in a key. A part of a picture can be drawn. Common Misconceptions No title Pictures are not drawn the same size No key given Example Sam asked his friends how they travelled to school. His results are shown in the table below. Transport Bus Car Walk Other Frequency Sam drew a pictogram to represent the results Key = 2 people Pictogram to show how Sam s friends travel to school Bus Car Walk The pictures should be identical in size, Other Example 2

9 Sue asked the pupils in her class what flavour crisps they liked. Her results are given below. Flavour crisps Ready Salted Salt and Chicken Other Vinegar Frequency Key = 4 people Pictogram to show pupils favourite flavour crisps Ready Salted Salt and Vinegar Chicken Other Drawing a Pie Chart. Strand Using Data Skills Element Present and analyse data

10 Interpret diagrams and graphs (Including pie charts) (Yr 7) Construct and interpret graphs and diagrams (including pie charts to represent discrete or continuous data with learners choosing an appropriate scale (Yr 9) A pie chart is a circle that is divided into sectors. Each sector represents part of the total. The larger the angle of the sector larger the frequency. Key Features A circle is used to represent all of the data. The pie chart must have a title Each sector must have a label or a key must be provided to aid the interpretation of the pie chart. When comparing pie charts the total sample size must be taken into account. Common Misconception No key No title The value for the frequency is used as the value for the angle to form the sector. Pupils find using a protractor difficult. The scale on the protractor will often require explanation. The angle of each sector is found by using the following formula Angle = Frequency x 360 Total Frequency Steps for drawing a pie chart. 1. Work out the angle for each item in the survey using the formula above. 2. Check that the angles add up to Draw the pie chart remembering to label each sector. Example The table below shows information about the holiday intentions of 600 people.

11 Holiday Camping Touring Seaside At Home Abroad Frequency Camping 100 x 360 = 60 Touring 120 x 360 = Seaside 170 x 360 = 102 At Home 60 x 360 = Abroad 150 x 360 = The protractor must be lined up correctly before measuring the angle. The centre of the protractor must but placed on Scatter Diagrams Strand Using Data Skills Element Present and analyse data

12 Construct graphs to represent data including scatter diagrams to investigate correlation (Yr 8) A Scatter Diagram is a graph in which one set of data is plotted on the horizontal axis and the other on the vertical axis. Scatter Diagrams are used to discover if there is a relationship (correlation) between the sets of data. Pupils are taught to recognise the correlation of scatter diagrams. Lines of Best Fit A line of best fit can be drawn on the graph to estimate values from the graph.

13 In Science the line of best fit is not necessarily a straight line rather it is the graph that best fits the points plotted and could be a curve. With this in mind when the topic is taught in mathematics lessons the differences in meaning of the lines of best fit are pointed out to the pupils. Key Features The data is represented by small crosses on the graph Every graph must have a title Both axes must have labels Common Misconceptions Inappropriate scale No title No label on the axes Example of a scatter diagram. Graph to show the correlation between outdoor temperature and therms of gas used in one house Averages Strand Element Using Data Skills Present and analyse data

14 Interpret results Use mean, median, mode and range to compare two distributions (discrete data) (Yr 7) Use mean, median, mode and range to compare two distributions (continuous data) (Yr 8) The term average is commonly used in everyday life but in fact there are three types of average: Mean, Median and Mode. In Maths the pupils are taught all three types of average from Year 7. Mean. The mean of a set of numbers is found by adding all of the values together and then dividing by the number of values. Median The median is the middle value of a set of data. It is found by firstly ordering (in ascending order) the values and then finding the middle of the data. [If there are two data values remaining then the two values are added together and the answer is divided by 2.] Mode The mode of a set of data is the value which occurs most often. [There can also be no mode, 2 modes, 3 modes etc.] Example. Find the mean, median and mode of the following set of data 24, 19, 32, 20, 23, 28, 27, 37, 30, 24 Mean Add up the values and divide by the number of values Median Place the numbers in ascending order , 24, 24, 27, 28, 30, 32, 37 = = 26.4 There are two middle numbers so the median is half way between = Mode The value that occurs most often 24 appears twice so 24 is the mode. Common Misconception Calculation errors (Mean)

15 Mis-counting the most common value (Mode) It is possible to have more than one mode (Mode) Not arranging the values into ascending order before selecting the middle value. (Median) Pupils do not learn the definitions thoroughly resulting in confusion Range The range finds the spread of the data set. It is found by subtracting the smallest value from the largest value. Range = Greatest Value Least Value Example Find the range of the following set of data 24, 19, 32, 20, 23, 28, 27, 37, 30, 24 Range = = 13