2. 1. Mean - easy to calculate but is affected by extreme values - to calculate use: Sum of all values Total number of values e.g. Calculate the mean of 6, 11, 3, 14, 8 6 + 11 + 3 + 14 + 8 5 Mean = = 42 5 Push equals on calculator BEFORE dividing = 8.4 e.g. Calculate the mean of 6, 11, 3, 14, 8, 100 Mean = 6 + 11 + 3 + 14 + 8 + 100 6 = 142 6 = 23.7 (1 d.p.)

3. 2. Median - middle number when all are PLACED IN ORDER (two ways) - harder to calculate but is not affected by extreme values a) for an odd number of values, median is the middle value e.g. Find the median of 39, 44, 38, 37, 42, 40, 42, 39, 32 32, 37, 38, 39, 39, 40, 42, 42, 44 To find placement of median use: n + 1 2 n = amount of data 9 + 1 = 10 = 5 2 2 OR Cross of data, one at a time from each end until you reach the middle value. b) for an even number of values, median is average of the two middle values e.g. Find the median of 69, 71, 68, 85, 73, 73, 64, 75 64, 68, 69, 71, 73, 73, 75, 85 n + 1 = 8 + 1 = 4.5 2 2 Median = 71 + 73 = 144 = 72 2 2 OR Median = 39

4. 3. Mode - only useful to find most popular item - is the most common value (can be none, one or more) e.g. Find the mode of 188, 93, 4, 93, 15, 0, 100 15 Mode = 15 and 93 Range - can show how spread out the data is - is the difference between the largest and smallest values e.g. Find the range of 4, 2, 6, 9, 8 highest valuelowest value Range = 9 – 2 Note: Its a good idea to write in brackets the values that make up the range. (2 – 9)= 7

5. - Useful when dealing with large amounts of discrete data e.g. Here are the number of fundraising tickets sold by 25 members of a Hockey team. Place data on a frequency table. 3, 5, 0, 1, 0, 2, 5, 2, 4, 0, 1, 2, 3, 5, 7, 2, 3, 3, 1, 4, 3, 3, 2, 0, 1 No. of tickets sold (x) TallyFrequency (f)x.f 0 1 2 3 4 5 6 7 Total IIII I II III I 4 4 5 6 2 3 1 25 0 x 4 = 0 1 x 4 = 4 2 x 5 = 10 3 x 6 = 18 4 x 2 = 8 5 x 3 = 15 00 7 x 1 = 7 62 To find the mean, we need the sum of the ticket numbers multiplied by their frequencies, and divide this by the total frequency. Mean = sum of x.f. total frequency = 62 25 = 2.48 tickets Check total frequency matches question!

6. No. of tickets sold (x) TallyFrequency (f)x.f 0 1 2 3 4 5 6 7 Total IIII I II III I 4 4 5 6 2 3 1 25 0 x 4 = 0 1 x 4 = 4 2 x 5 = 10 3 x 6 = 18 4 x 2 = 8 5 x 3 = 15 00 7 x 1 = 7 62 To find the median, determine its position by using the previous formula. n + 1 = 25 + 1 = 13 2 2 Now, by adding down the frequency column, locate position of median 4 8 13 Therefore: Median = 2 tickets To find the mode, look for the highest frequency Therefore: Mode = 3 tickets

7. 1. Discrete Data – usually found by counting, usually whole numbers e.g.Number of cars passing the school 2. Continuous Data – usually found by measuring e.g.Weights and heights of students 1. Bar Graph – shows discrete data – must have GAPS between bars Number of dinnersFrequency 02 16 28 36 44 52 e.g. Beside are the number of times 28 students went out for dinner last month. Place data on a bar graph.

8. Don’t forget a title Or axis labels Note gaps between bars

9. 2. Dot Plots – are like a bar graph – each dot represents one item e.g. Plot these 15 golf scores on a dot plot 70, 72, 68, 74, 74, 78, 77, 70, 72, 72, 76, 72, 76, 75, 78 Range plot between lowest and highest values

10. 3. Pictograms – uses symbols to represent fixed numbers – key shows the value of the symbol e.g. Using an appropriate symbol, draw a pictogram displaying the number of hours per week spent completing homework for the following subjects. Hours of Study in a Week Science English Maths KEY 1 hour

11. 4. Pie Graphs – show comparisons – slices are called sectors – uses percentages and angles (protractor and compass) e.g.Students of a class arrived to school in the following manner. Show on a Pie Graph Walked = 6 Cycled = 5 Car = 4 Bus = 9 To calculate angle of sectors use: Amount of sector x 360 Total Data Walked = 6 x 360 = 90 24 75°135°60°90° Student Mode of Transport Cycled WalkedCar Bus Note: Instead of labels, a key could also be used.

12. 5. Strip Graph – shows the proportion of each part to the whole – should have a scale – linked to pie graphs e.g.Using Pie Graph example, Strip Graph drawn could use a scale of1 cm = 2 students – are measures of spread which with the median splits the data into quarters – method used is similar as to when finding median When the data is in order: – the lower quartile (LQ) has – the upper quartile (UQ) has 25% or ¼ 75% or ¾ of the data below it. – the Interquartile Range (IQR) =UQ – LQ

13. e.g. Find the LQ, UQ and the interquartile range of the following data 6, 6, 6, 7, 8, 9, 10, 10, 11, 14, 16, 16, 17, 19, 20, 20, 24, 24, 25, 29 Note: always find the median first20 + 1 = 21 = 10.5 2 2 10 + 1 = 11 = 5.5 2 2 ORLQ =8 + 9 = 17 = 8.5 2 2 UQ = 20 + 20 = 40 = 20 2 2 OR e.g. Find the LQ, UQ and the interquartile range of the following data 5, 6, 8, 10, 11, 11, 12, 15, 18, 22, 23, 28, 30 Remember, always find the median first13 + 1 = 14 = 7 2 2 or cross off data As the median is an actual piece of data, it is ignored when finding the LQ and UQ 6 + 1 = 7 = 3.5 2 2 LQ = 8 + 10 = 18 = 9 2 2 UQ = 22 + 23 = 45 = 22.5 2 2 IQR = UQ - LQIQR = 20 – 8.5 = 11.5 IQR =22.5 – 9 = 13.5

14. – records and organises data – most significant figures form the stem and the final digits the leaves – can be in back to back form in order to compare two sets of data e.g. Place the following heights (in m) onto a back to back stem and leaf plot BOYS = 1. 59, 1.69, 1.47, 1.43, 1.82, 1.70, 1.73, 1.35, 1.76, 1.68, 1.62, 1.84, 1.45, 1.50, 1.54, 1.73, 1.84, 1.71, 1.66 GIRLS = 1. 44, 1.46, 1.63, 1.29, 1.48, 1.57, 1.51, 1.42, 1.34, 1.45, 1.57, 1.59, 1.42 Unordered Graph of Heights Ordered Graph of Heights Boys Girls Boys Girls 1.8 1.8 1.7 1.7 1.6 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 Look at the highest and lowest data values to decide the range of the stem Place the final digits of the data on the graph on the correct side,7,9,3,2,0,3 5,6,8,2 4 5,0 4,3 1 6,4 4,6, 3 9 8, 7,1, 2, 4 5, 7,9 2 4, 4, 2 6, 3, 3, 1, 0 9, 8, 6, 2 9, 4, 0 7, 5, 3 5 3 1, 7, 7, 9 2, 2, 4, 5, 6, 8 4 9

15. Graph of Heights Boys Girls 1.8 1.7 1.6 1.5 1.4 1.3 1.2 4, 4, 2 6, 3, 3, 1, 0 9, 8, 6, 2 9, 4, 0 7, 5, 3 5 3 1, 7, 7, 9 2, 2, 4, 5, 6, 8 4 9 e.g. From the ordered plot state the minimum, maximum, LQ, median, UQ, IQR and range statistics for each side BOYSGIRLS Minimum: Maximum: LQ: Median: UQ: IQR: Range: For each statistic, make sure to write down the whole number, not just the ‘leaf’! 1.29 m 1.63 m 1.63 – 1.29 = 0.34 m Median = 13 + 1 = 7 2 When finding median, LQ and UQ, make sure you count/cross in the right direction! LQ/UQ = 6 + 1 = 3.5 2 1.42 m 1.46 m 1.57 m 1.57 – 1.42 = 0.15 m Remember: If you find it hard to calculate stats off graph, write out data in a line first! 1.35 m 1.84 m 1.50 m 1.68 m 1.73 m 1.73 – 1.50 = 0.23 m 1.84 – 1.35 = 0.49 m

16. – shows the minimum, maximum, LQ, median and UQ – ideal for comparing two sets of data e.g. Using the height data from the Stem and Leaf diagrams, draw two box and whisker plots (Boys and Girls) Note: Use the minimum and maximum values to determine length of scale Males Females Question: What is the comparison between the boy and girl heights? ANSWER? MinimumLQMedianUQMaximum EVIDENCE? Box and Whisker Plot of Boys and Girls Heights

17. – used when dealing with a large amount of continuous data and groups are needed e.g. Listed below are the heights (in cm) of 25 students. Represent the data on a frequency table 167, 173, 171, 149, 162, 174, 185, 165, 160, 170, 173, 161, 158, 172, 168, 168, 178, 170, 180, 166, 183, 150, 164, 161, 164 IntervalTallyFreq. (f)Midpoint (x)x.f 140 – 149 150 – 159 160 – 169 170 – 179 180 – 189 TOTAL To calculate the mean a midpoint is needed and the formula used is: e.g. Calculate the mean from the above data and state the modal interval I II IIII IIII I IIII III III 1 2 11 8 3 25 (140 + 149) / 2144.5 154.5 164.5 174.5 184.5 144.5 x 1144.5 309 1809.5 1396 553.5 4212.5 Mean =4212.5 25 = 168.5 cmModal Interval =160 – 169 cm Note: Make sure you have enough groups but don’t make them too small!

18. – display grouped data – frequency is along vertical axis, group intervals are along horizontal axis – there are NO gaps between bars e.g. Graph the grouped frequency table data about heights onto a histogram Note: The groups from the table form the intervals along the horizontal axis and the highest frequency determines the height of the vertical axis.

19. – Side by side histograms can also be used to compare data Question: What is the comparison between the female and male heights? ANSWER? EVIDENCE?

20. – looks for a relationship between two measured variables – points are plotted like co-ordinates e.g. Below are the heights and weights of Year 7 boys. Place on a scatter plot. Height (cm) Weight (kg) 14448 15252 16150 14849 15553 14047 15858 13945 14750 15051 15249 13846 13744 14549 Use the data to determine scale to use on both axes If points form a line (or close to) we can say there is a relationship between the two variables. Line of best fit Outliers can generally be ignored What is the relationship between the boys height and weight? ANSWER? EVIDENCE?

21. – a collection of measurements recorded at specific intervals where the quantity changes with time. Features of Time Series a) Order is important with all measurements retained to examine trends b) Long term trends where measurements definitely tend to increase or decrease c) Seasonal trends resulting in up and down patterns e.g. Draw a time series graph for the following data: SeasonQuarterly sales Sept.9040 Dec.8650 Mar. 968370 June9250 Sept.9033 Dec.8578 Mar. 978495 June9407 Sept.9209 Dec.8740 Mar. 988618 June9504 Sept.9246 Dec.8929 Mar. 998670 Join up each of the points What are the short and long term trends? ANSWER?EVIDENCE?

22. Good graphs should have: - an accurate heading (watch emotive headings) - scales in even steps - scales from zero unless a break is shown - values easy to read - bar graphs have the same width bars and similar shading Sample:When part of the group is surveyed Census:Whole population is surveyed Population:The entire group of members under consideration Survey:Collection of information from some or all members of a population Sampling Frame:A list covering the target population A Good Sampling Frame:- should have each unit listed only once - has each unit distinguishable from others - is up to date

23. When planning an investigation: - think carefully about what you are trying to find (question) - what data is needed - how will you obtain the data - is the method practical and convenient - how will you record the information - how will you present the data

24. A sample should: 1) Be large enough to be representative of whole population 2) Have people/items in it that are representative of the population It is best to choose samples that are large and random but size may be affected by time, money, personnel, equipment etc. Simple random sampling: 1- obtain a population list 2- number each member 3- use random table or random number on calculator Systematic sampling: 1- obtain a population list 2- randomly select a starting point on the list 3- select every nth member until desired sample size is reached Note: every nth member is found by:Population/group size Size of sample needed

25. - Biased sample - Wrong measurements - Poorly worded, misleading questions - Mistakes in calculations and/or display For when comparing two sets of data. 1. If the two sets of data are NOT related (have no affect on each other) Use the wordsCOMPAREORCOMPARISON e.g. What is theCOMPARISONbetween… How does …COMPAREto … THEN: (also if justifying statements) - Get as many statistics as possible (averages, quartiles, max and min, range etc) - Draw aSTEM and LEAF GRAPHand a BOX and WHISKER PLOT (maybeSIDE BY SIDE HISTOGRAMS) - Answer your question in one sentence - Back up your answer with at least 2-3 statements using the data from your statistics/graphs (at least one each on average and spread) Remember to use “generally/on average”

26. 2. If the two sets of data ARE related (do have an affect on each other) Use the wordsRELATEORRELATIONSHIP e.g. What is theRELATIONSHIPbetween… How does …RELATEto … THEN: - Get as many statistics as possible - Draw aSCATTERPLOT - Answer your question in one sentence - Back up your answer with at least 2-3 statements 3. If it is a single set of data taken over time we look for short and long term trends. - Write your question in the following manner: What are theSHORTandLONG TERMtrends in …. THEN: - Get as many statistics as possible - Draw aTIME SERIES GRAPH - Answer your question and back it up with justifications

27. 1. In terms of Data Collection Typical Limitations Improvements - Sample too small - Not random or representative - Outliers distort data - Get a representative sample - Taken over too short a time period - Take data over a longer time period - Obtain a bigger sample - Ignore extreme outliers 2. In terms of Your Process Typical Limitations Improvements - Not enough statistics calculated - Calculate more statistics - Not enough graphs used, data could be compared better - Use other graphs (i.e. comparative histograms) - Scales on graphs too large- Change scales on graph (smaller) - Way graphs are drawn- Alter the way the graphs may be drawn