Data Handling & Averages chapter concept of 11 plus exam GL assessment examination
Data Handling & Averages FROM PREVIOUS YEAR GL ASSESSMENT QUESTIONS 11 plus exam, Maths ,based on GL assessment examination
#### **1. Averages (Mean, Median, Mode, Range)** The "average" usually means the **Mean**, but there are three main types. **a) The Mean (The Average)** * **Concept:** It's the total of all values divided by the number of values. * **When to use:** When the data is spread out and doesn't have many repeated numbers. * **Formula:** `Mean = (Sum of all values) ÷ (Number of values)` * **Example:** Find the mean of 5, 7, 3, and 9. * Step 1: Sum = 5 + 7 + 3 + 9 = **24** * Step 2: Number of values = **4** * Step 3: Mean = 24 ÷ 4 = **6** **b) The Median (The Middle Value)** * **Concept:** It's the middle number when all values are put in order. * **When to use:** When there are extreme values (very high or very low) that could make the mean misleading. * **How to find it:** 1. Put the numbers in order from smallest to largest. 2. Find the middle number. 3. If there are two middle numbers, find the mean of those two. * **Example 1 (Odd amount):** Find the median of 12, 3, 7. * Order: 3, 7, 12. The middle number is **7**. * **Example 2 (Even amount):** Find the median of 15, 3, 9, 1. * Order: 1, 3, 9, 15. The two middle numbers are 3 and 9. * Median = (3 + 9) ÷ 2 = 12 ÷ 2 = **6** **c) The Mode (The Most Frequent)** * **Concept:** It's the value that appears most often. * **When to use:** When you need to know the most popular or common item. There can be one mode, more than one mode, or no mode at all. * **Example:** Find the mode of 5, 7, 5, 2, 8, 5. * The number 5 appears three times. The mode is **5**. **d) The Range (The Spread)** * **Concept:** It's the difference between the largest and smallest values. * **Formula:** `Range = Largest Value - Smallest Value` * **Example:** Find the range of 4, 10, 3, 7. * Largest = 10, Smallest = 3. * Range = 10 - 3 = **7** --- #### **2. Reading and Interpreting Data** **a) Bar Charts and Dual Bar Charts** * **Concept:** Uses bars of different heights or lengths to show data. The taller the bar, the larger the value. * **How to read:** * Always check the **title** and the **labels** on both axes (the horizontal and vertical lines). * Look at the **scale** carefully. Is it going up in 1s, 2s, 5s, 10s? * **Dual Bar Charts:** Used to compare two different sets of data for the same categories (e.g., boys vs girls, 2022 vs 2023). **b) Pie Charts** * **Concept:** A circle divided into sectors. The size of each sector shows the proportion of the whole. * **Key Fact:** The whole pie chart represents **100%** or the **total sum**. * **How to read:** * Often, you will be asked to find out how many degrees represent one item. * Remember: A full circle is **360°**. * If a pie chart shows favourite fruits and the 'Apple' section is a 90° angle, what fraction is that? 90°/360° = 1/4. **c) Line Graphs** * **Concept:** Uses points connected by lines to show data, often over **time**. * **How to read:** * The horizontal axis is often time (days, months, years). * An upward slope means the values are **increasing**. * A downward slope means the values are **decreasing**. * A flat line means the values are **staying the same**. **d) Pictograms** * **Concept:** Uses pictures or symbols to represent data. * **How to read:** * **CRUCIAL:** Check the **key** to see what each symbol represents. One symbol might stand for 1 person, 10 people, or 100 people. * Sometimes a **half-symbol** is used. **e) Two-way Tables** * **Concept:** A table that shows the relationship between two categories. * **How to read:** * Look at the row and column headings carefully. * The totals at the end of each row and column are very important. They often help you find a missing number. * Example: A table showing `Boys/Girls` vs `Walk/Cycle`. --- ### **Part 2: Practice Questions (Modelled on GL Assessment Style)** Here are 50+ questions covering all the sub-topics. #### **Section A: Averages & Range (15 Questions)** 1. Find the mean of these numbers: 8, 12, 5, 3, 2. 2. Find the median of these numbers: 15, 4, 9, 1, 7. 3. What is the mode of these numbers: 6, 2, 6, 4, 1, 2, 6? 4. Calculate the range of these numbers: 21, 17, 35, 19, 22. 5. The mean of four numbers is 7. Three of the numbers are 4, 9, and 7. What is the fourth number? 6. The test scores of five students are: 85, 90, 78, 92, and x. If the mean score is 87, what is the value of x? 7. Find the median of: 25, 30, 22, 27, 31, 38. 8. What is the range of the ages: 11, 12, 11, 13, 12, 11, 14? 9. A footballer scores the following number of goals in 5 matches: 2, 0, 3, 1, 4. What is her mean number of goals per match? 10. The temperatures in Slough over a week were: 18°C, 22°C, 21°C, 19°C, 23°C, 24°C, 17°C. What is the range of the temperatures? 11. The mode of five numbers is 4. The median is 5. The mean is 6. What could the five numbers be? (Find one possible set) 12. The mean of three numbers is 10. The range is 12. The two smallest numbers are the same. What are the three numbers? 13. Find the mean, median, and mode of: 5, 7, 5, 2, 8, 5, 1. 14. If the range of a set of six numbers is 9 and the smallest number is 6, what is the largest number? 15. The median of four numbers is 6.5. The four numbers are 4, x, 9, y. Find a possible value for x and y. #### **Section B: Bar Charts & Dual Bar Charts (10 Questions)** *Use the following bar chart description for Q16-20:* A bar chart titled "Favourite Subjects of Year 6" has the following bars: Maths (20 pupils), English (15 pupils), Science (25 pupils), History (10 pupils), Art (15 pupils). 16. How many pupils chose Science as their favourite subject? 17. What is the total number of pupils represented in the chart? 18. What is the range of the number of pupils choosing a subject? 19. What is the mean number of pupils per subject? 20. Which subject is the mode? *Use the following dual bar chart description for Q21-25:* A dual bar chart shows "Sports Team Membership". For Football, Boys=12, Girls=8. For Netball, Boys=2, Girls=15. For Cricket, Boys=10, Girls=5. For Swimming, Boys=7, Girls=10. 21. How many boys are in the football team? 22. How many girls play netball? 23. Which sport has the most members in total? 24. What is the total number of children represented in the chart? 25. What is the difference between the total number of boys and the total number of girls in these sports teams? #### **Section C: Pie Charts (10 Questions)** 26. A pie chart is divided into 4 equal sections. What angle is each section? 27. In a pie chart showing how 36 children travel to school, 18 children walk. What angle of the pie chart represents 'Walk'? 28. A pie chart has a section of 108°. If the total number of people surveyed is 60, how many people does the 108° section represent? 29. The favourite colours of a class are shown in a pie chart. The 'Blue' section is 90°. If 10 people chose blue, how many people are in the class altogether? 30. A survey of 40 people's favourite fruit is drawn as a pie chart. How many degrees represent each person? 31. In a pie chart, a sector of 60° represents 5 people. How many people does the whole pie chart represent? 32. A pie chart is split into three sectors: 120°, 150°, and 90°. What fraction of the total does the 90° sector represent? 33. If 1/5 of a pie chart is shaded, what is the angle of the shaded sector? 34. A pie chart angle is 72°. What fraction of the total is this? 35. In a pie chart for 90 people, the 'Pizza' section is 160°. How many people prefer pizza? #### **Section D: Line Graphs (8 Questions)** *Use the following description for Q36-40:* A line graph shows Tom's savings over 6 months: Jan: £20, Feb: £30, Mar: £40, Apr: £35, May: £50, Jun: £60. 36. How much did Tom save in March? 37. Between which two months did his savings decrease? 38. What was the total amount he saved over the 6 months? 39. What was the range of his savings over this period? 40. What was the mean amount he saved per month? 41. A line graph shows the temperature throughout a day. It starts at 5°C at 6 am, rises to 15°C at 12 pm, rises to 18°C at 3 pm, and falls to 10°C at 10 pm. What was the highest temperature? 42. The same graph as Q41: When was the temperature 15°C? 43. The same graph as Q41: What was the temperature increase from 6 am to 3 pm? #### **Section E: Pictograms (7 Questions)** *Use the following description for Q44-48:* A pictogram shows "Books Read in a Week". Each picture of a book equals 4 books read. * Anna: 🕮🕮🕮 * Ben: 🕮🕮 * Chloe: 🕮🕮🕮🕮 * David: 🕮 44. How many books did Anna read? 45. How many books did Ben read? 46. Who read exactly 16 books? 47. What is the total number of books read by all four children? 48. What is the mean number of books read per child? 49. In a different pictogram, a symbol represents 5 cars. If a row has 3 and a half symbols, how many cars does it represent? 50. A pictogram uses a star to represent 2 goals. If a team has 7 stars, how many goals did they score? --- ### **Part 3: 10 Questions from a Previous GL Style Paper (with Solutions)** These questions are representative of the style and difficulty you can expect. **Q1.** The mean of four numbers is 8. Three of the numbers are 2, 9, and 11. What is the fourth number? **Q2.** The bar chart below shows the number of ice creams sold each day from Monday to Friday. On Monday, 40 were sold; Tuesday, 60; Wednesday, 30; Thursday, 50; Friday, 70. What was the mean number of ice creams sold per day? **Q3.** What is the median of the following set of numbers: 13, 11, 15, 18, 12, 17? **Q4.** The pictogram shows the number of apples picked by children. Each apple symbol stands for 5 apples. Sarah has 4 symbols, James has 3 symbols, and Lily has 5 symbols. How many apples did they pick in total? **Q5.** The range of a set of five numbers is 7. The smallest number is 4. What is the largest number? **Q6.** In a pie chart, an angle of 120° represents 30 people. How many people does the whole pie chart represent? **Q7.** The line graph shows the height of a plant over 5 weeks. In Week 1 it was 10cm, Week 2 it was 15cm, Week 3 it was 20cm, Week 4 it was 22cm, Week 5 it was 25cm. What was the increase in height from Week 1 to Week 5? **Q8.** The mode of these numbers is 7: 4, 7, 3, 7, 2, x. What is a possible value for x? **Q9.** A two-way table shows how Year 6 children travel to school. | | Walk | Car | Cycle | |-------|------|-----|-------| | Boys | 10 | 12 | 8 | | Girls | 15 | 8 | 7 | How many more boys than girls travel by car? **Q10.** The mean of five numbers is 6. After a sixth number is added, the mean becomes 7. What is the sixth number? --- ### **Answer Key & Solutions** #### **Section A: Averages & Range** 1. (8+12+5+3+2)/5 = 30/5 = **6** 2. Order: 1, 4, 7, 9, 15. Median = **7** 3. **6** (appears 3 times) 4. 35 - 17 = **18** 5. Total for 4 numbers = 4 x 7 = 28. Total of known three = 4+9+7=20. Fourth number = 28-20=**8** 6. Total for 5 scores = 5 x 87 = 435. Total of known four = 85+90+78+92=345. x = 435-345=**90** 7. Order: 22, 25, 27, 30, 31, 38. Median = (27+30)/2 = 57/2 = **28.5** 8. 14 - 11 = **3** 9. (2+0+3+1+4)/5 = 10/5 = **2** 10. 24 - 17 = **7** 11. One possible set: **4, 4, 5, 7, 10** (Mode=4, Median=5, Mean=(4+4+5+7+10)/5=6) 12. If the two smallest are the same, and the mean is 10, the total is 30. If the range is 12, the largest - smallest = 12. Let the numbers be x, x, y. So 2x + y = 30 and y - x = 12. Solving: y = x+12. 2x + (x+12)=30 -> 3x=18 -> x=6. y=18. Numbers are **6, 6, 18**. 13. Order: 1, 2, 5, 5, 5, 7, 8. Mean=33/7≈4.71, Median=**5**, Mode=**5** 14. Largest = Smallest + Range = 6 + 9 = **15** 15. For median 6.5, the two middle numbers must average to 6.5. We have 4 and 9. The middle two numbers when ordered will be x and 9 (or 4 and y). So (x+9)/2=6.5 -> x+9=13 -> x=4. But then numbers are 4, 4, 9, y. The middle two are 4 and 9, average is 6.5. y can be any number ≥9. So one possibility: x=4, y=10. #### **Section B: Bar Charts** 16. **25** 17. 20+15+25+10+15 = **85** 18. 25 - 10 = **15** 19. 85 ÷ 5 = **17** 20. **Science** (25 is the highest) 21. **12** 22. **15** 23. Football: 12+8=20. Netball: 2+15=17. Cricket: 10+5=15. Swimming: 7+10=17. **Football** 24. Boys total: 12+2+10+7=31. Girls total: 8+15+5+10=38. Total = 31+38=**69** 25. Boys=31, Girls=38. Difference = 38-31 = **7** (more girls) #### **Section C: Pie Charts** 26. 360° ÷ 4 = **90°** 27. 18/36 = 1/2 of the total. 1/2 of 360° = **180°** 28. (108°/360°) x 60 = (3/10) x 60 = **18 people** 29. 90° represents 10 people. 360° represents (360/90) x 10 = 4 x 10 = **40 people** 30. 360° ÷ 40 = **9°** 31. 60° represents 5 people. 360° represents (360/60) x 5 = 6 x 5 = **30 people** 32. 90°/360° = **1/4** 33. 1/5 of 360° = **72°** 34. 72/360 = **1/5** 35. (160°/360°) x 90 = (4/9) x 90 = **40 people** #### **Section D: Line Graphs** 36. **£40** 37. **March to April** (£40 to £35) 38. 20+30+40+35+50+60 = **£235** 39. £60 - £20 = **£40** 40. £235 ÷ 6 = **£39.17** 41. **18°C** 42. **12 pm** (and possibly other times, but 12 pm is the clear answer from the data) 43. 18°C - 5°C = **13°C** #### **Section E: Pictograms** 44. 3 x 4 = **12** 45. 2 x 4 = **8** 46. Chloe (4 x 4 = **16**) 47. Anna:12, Ben:8, Chloe:16, David:4. Total = 12+8+16+4=**40** 48. 40 ÷ 4 = **10** 49. (3 x 5) + (0.5 x 5) = 15 + 2.5 = **17.5 cars** 50. 7 x 2 = **14 goals** #### **GL Style Paper Solutions** **A1.** Total for 4 numbers = 4 x 8 = 32. Total of known three = 2+9+11=22. Fourth number = 32-22=**10**. **A2.** Total = 40+60+30+50+70=250. Mean = 250 ÷ 5 = **50**. **A3.** Order: 11, 12, 13, 15, 17, 18. Median = (13+15)/2 = 28/2 = **14**. **A4.** Total symbols = 4+3+5=12. Total apples = 12 x 5 = **60**. **A5.** Largest = Smallest + Range = 4 + 7 = **11**. **A6.** 120° represents 30 people. 360° represents (360/120) x 30 = 3 x 30 = **90 people**. **A7.** 25cm - 10cm = **15cm**. **A8.** For the mode to be 7, 7 must appear most often. It already appears twice. If x=7, it appears three times, which is the most. So **7** is a possible value. **A9.** Boys by car = 12. Girls by car = 8. Difference = 12-8 = **4**. **A10.** Total of first five numbers = 5 x 6 = 30. Total of all six numbers = 6 x 7 = 42. The sixth number = 42 - 30 = **12**. Good luck with your preparation ### **Section A: Averages & Range (10 More Questions)** 1. Find the mean of 15, 22, 18, 25, and 10. 2. The median of five numbers is 12. Four of the numbers are 7, 15, 9, and 13. What is the fifth number? 3. What is the mode of this set: 4, 5, 6, 4, 7, 8, 5, 4, 9? 4. The range of a set of numbers is 8. If the smallest number is 3, what is the largest number? 5. The mean of six numbers is 20. Five of the numbers are 18, 22, 19, 21, and 25. What is the sixth number? 6. Find the median of: 41, 35, 47, 38, 42, 39, 45. 7. A cricketer's scores over 6 innings are: 32, 0, 45, 28, 51, 36. What is his mean score? 8. The mode of four numbers is 5. Their mean is 6. What could the four numbers be? (Give one possible set) 9. The mean age of three children is 11. The range of their ages is 4. What are their ages? (Give one possible set) 10. The mean of four numbers is 15. When a fifth number is added, the mean becomes 17. What is the fifth number? ### **Section B: Bar Charts & Dual Bar Charts (10 More Questions)** *Use the following chart description for Q11-15:* A dual bar chart shows "Pets owned by Year 6". Cats: Boys=8, Girls=12. Dogs: Boys=10, Girls=10. Fish: Boys=5, Girls=3. Rabbits: Boys=2, Girls=6. 11. How many girls own cats? 12. How many boys own dogs or fish? 13. What is the total number of pets recorded? 14. What is the difference between the number of cat owners and rabbit owners? 15. What is the mean number of pets per type (for the four pet types listed)? *Use this data for Q16-20:* A single bar chart shows "Ice-cream Sales": Monday=25, Tuesday=40, Wednesday=35, Thursday=50, Friday=60. 16. On which day were sales 35? 17. What was the total number of sales from Monday to Friday? 18. What was the mean daily sale? 19. What was the range of the daily sales? 20. If Saturday's sales were double Friday's, how many were sold on Saturday? ### **Section C: Pictograms (10 More Questions)** *Use this pictogram for Q21-25:* **Favourite Sandwiches** (Each 🥪 = 4 votes) - Cheese: 🥪🥪🥪 - Ham: 🥪🥪🥪🥪 - Tuna: 🥪🥪 - Egg: 🥪 21. How many people voted for ham? 22. How many more people voted for cheese than egg? 23. What was the total number of votes? 24. What was the mean number of votes per sandwich type? 25. If 8 more people voted and all chose tuna, how many tuna symbols would there be? 26. In a pictogram, a symbol represents 3 houses. How many houses are represented by 7 symbols? 27. A row in a pictogram has 2 and a half stars. If each star represents 6 goals, how many goals are shown? 28. A pictogram showing books read uses a book symbol for 5 books. Sarah has 4 symbols. How many books did she read? 29. In a survey about transport, a car symbol equals 10 people. If 4 people are represented by a part of a symbol, what fraction of a car symbol is used? 30. A pictogram has 5 complete symbols and 1 half symbol. If each symbol represents 8 items, how many items are there? ### **Section D: Pie Charts (10 More Questions)** 31. A pie chart is divided into 8 equal sections. What is the angle of each section? 32. In a pie chart showing favourite subjects, the Maths section is 90°. If 15 people chose Maths, how many people were surveyed in total? 33. A pie chart angle of 120° represents 24 people. How many people does a 30° angle represent? 34. In a pie chart for 48 people, how many degrees represent each person? 35. 1/8 of a pie chart is shaded. What is the angle of the shaded section? 36. A pie chart has sections of 100°, 120°, and 140°. What fraction of the chart is the 100° section? 37. The favourite fruit of 60 people is shown in a pie chart. The 'Apple' section is 150°. How many people prefer apples? 38. A sector of 72° represents 6 people. How many people are represented by the rest of the pie chart (288°)? 39. In a pie chart, the ratio of one sector to the whole chart is 1:6. What is the angle of that sector? 40. A pie chart is split into 5°, 85°, 90°, 100°, and 80° sectors. Is this possible? Why? ### **Section E: Line Graphs (10 More Questions)** *Use this data for Q41-45:* A line graph shows plant growth: Week 1=2cm, Week 2=4cm, Week 3=7cm, Week 4=9cm, Week 5=12cm. 41. How much did the plant grow in Week 3? 42. Between which two weeks was the growth the greatest? 43. What was the mean weekly growth over the 5 weeks? 44. What was the range of the heights over the 5 weeks? 45. If the growth continues by the same amount from Week 4 to Week 5, what would the height be in Week 6? *Use this data for Q46-50:* A line graph shows the temperature in a day: 7am=5°C, 9am=8°C, 11am=12°C, 1pm=14°C, 3pm=16°C, 5pm=13°C. 46. What was the temperature at 1pm? 47. When was the temperature 12°C? 48. What was the increase in temperature from 7am to 3pm? 49. During which period did the temperature decrease? 50. What was the temperature range during the day? --- ### **Fictional "Previous Year Paper" (50 Questions)** **This section mimics a full GL Assessment paper section.** 1. Calculate: 345 + 278 2. What is 7² - 3³? 3. Write 0.625 as a fraction in its simplest form. 4. What is 15% of 340? 5. Find the mean of 12, 17, 14, 11, 16. 6. A packet of biscuits costs £1.20. How much do 5 packets cost? 7. A rectangle is 12cm long and 5cm wide. What is its perimeter? 8. What is the area of the rectangle in Q7? 9. A box holds 24 pencils. How many boxes are needed for 150 pencils? 10. What is the missing number: 4, 9, 16, 25, ?, 49 11. A train leaves at 14:25 and arrives at 16:08. How long is the journey? 12. Simplify the ratio 18:24 13. Share £45 in the ratio 2:3 14. What is 3/5 of 60? 15. A book has 240 pages. Sarah reads 35% of it. How many pages are left? 16. Find the median of 8, 3, 9, 2, 7, 1 17. The range of a set of numbers is 5. The smallest is 2. What is the largest? 18. In a pictogram, a symbol represents 4 houses. 7 symbols represent how many houses? 19. A pie chart has a 90° sector. What fraction of the whole is this? 20. A bat costs £15 more than a ball. The total cost is £25. How much is the ball? 21. A number is multiplied by 3 and then 7 is added. The result is 22. What is the number? 22. What is the next number: 1, 3, 6, 10, 15, ? 23. A bus carries 52 passengers. How many buses for 310 passengers? 24. A square has a perimeter of 36cm. What is its area? 25. 3/8 of a number is 21. What is the number? 26. Find the mode of 5, 7, 2, 5, 9, 7, 1, 5 27. The mean of three numbers is 10. Two numbers are 8 and 12. What is the third? 28. A recipe for 4 needs 200g flour. How much for 10? 29. A film is 1 hour 50 minutes long. It starts at 19:30. When does it finish? 30. What is the probability of rolling an even number on a fair dice? 31. A shirt was £40. It's reduced by 15%. What is the sale price? 32. Write 4/5 as a percentage. 33. Solve: 3x + 7 = 22 34. A triangle has angles of 50° and 60°. What is the third angle? 35. A pack of 6 yoghurts costs £2.40. What is the cost per yoghurt? 36. A car uses 8 litres for 100km. How far on 20 litres? 37. 7.2 ÷ 0.8 = ? 38. A cube has a volume of 64cm³. What is the length of one side? 39. 3/4 + 2/5 = ? 40. 5.06 × 1000 = ? 41. A bag has 3 red, 2 blue, 1 green marble. Probability of red? 42. 0.3 as a fraction? 43. 15% as a decimal? 44. 2³ × 3² = ? 45. 1 mile ≈ 1.6 km. 5 miles ≈ ? km 46. A TV costs £320 + 20% VAT. What's the total? 47. 7/10 - 2/5 = ? 48. 360 ÷ 12 = ? 49. 5.7 + 3.89 = ? 50. A number divided by 4 is 9. What's the number? --- ### **50 More Questions from Previous Year GL Assessment Styles** **Mixed application questions focusing on data handling and number.** 51. The mean of five numbers is 12. Four are 10, 14, 11, 13. Find the fifth. 52. A bar chart shows rainfall: Jan=40mm, Feb=35mm, Mar=50mm, Apr=45mm. Mean rainfall? 53. A pictogram symbol = 3 trees. 5 symbols = ? trees 54. A pie chart sector of 60° represents 5 people. Total people? 55. Line graph: 9am=10°C, 12pm=16°C, 3pm=18°C, 6pm=14°C. Temperature range? 56. Median of 21, 25, 18, 23, 27, 19, 22 57. Mode of 4, 2, 5, 4, 6, 3, 4, 7 58. Range of 7, 3, 9, 5, 6, 4 59. Dual bar chart: Football-Boys=15, Girls=5; Tennis-Boys=8, Girls=12. Total in tennis? 60. In Q59, how many more boys than girls play football? 61. Pictogram: 🎮=2 hours. Tom: 🎮🎮🎮🎮. Hours played? 62. Pie chart has 6 equal sectors. Angle per sector? 63. Line graph profit: Jan=£100, Feb=£150, Mar=£120, Apr=£180. Mean profit? 64. Mean of 8, 12, 5, ?, 10 is 9. Find missing number. 65. Median of 7, 3, 9, 5, 2, 8, 4 66. Range is 11, smallest is 4. Largest? 67. Bar chart: Class 6A=28 pupils, 6B=32, 6C=25. Total pupils? 68. In Q67, mean per class? 69. Pictogram: ❤️=5 likes. Post has 4.5 hearts. Likes? 70. Pie chart: 90° sector = 1/4 of total. True/False? 71. Line graph shows consistent increase from day1=50 to day5=90. Day3 value? 72. Mean age of 4 children is 9. Total age? 73. Median of even number set 12, 15, 18, 20 74. Mode of 1, 3, 1, 4, 3, 1, 5 75. Dual bar chart: Swimming-Boys=10, Girls=15; Gym-Boys=12, Girls=8. Total girls? 76. In Q75, which activity is more popular with boys? 77. Pictogram key missing. 18 items shown with 6 symbols. Each symbol = ? 78. Pie chart total 72 people. 45° sector represents ? people. 79. Line graph: steady decline from 100 to 40 over 6 hours. Drop per hour? 80. Mean of 5, 10, 15, 20, x is 14. Find x. 81. Median of 25, 30, 22, 27, 35 82. Range of 45, 32, 56, 41, 39 83. Bar chart scale: each line = 5 units. Bar reaches 4 lines = ? units. 84. Dual bar chart difference: Hockey B=14, G=10. Difference? 85. Pictogram half symbol = 2.5 items. 3 full + 1 half = ? items. 86. Pie chart 180° sector = ? of whole. 87. Line graph plateaus at y=25 for 3 readings. Means value ?. 88. Mean of three numbers is 8. Their total is ? 89. Median of 6, 2, 9, 1, 7, 4, 3 90. Mode of 5, 5, 3, 3, 5, 2, 3 (bimodal) 91. Range of 12, 7, 15, 9, 11, 5 92. Bar chart title missing. Shows fruit on x-axis, number on y. Title? 93. Dual bar chart totals: Art B=9, G=11; Music B=7, G=13. Total participants? 94. Pictogram symbol change: was =4, now =5. Old 5 symbols = new ? symbols. 95. Pie chart total people 40. 90° sector = ? people. 96. Line graph: rapid rise then slow fall. Description matches? 97. Mean calculation: (10+15+20+25)/4 = ? 98. Median of single number 7. 99. Range of identical numbers 5,5,5,5. 100. Data handling question typically asks for? --- ### **COMPREHENSIVE ANSWER KEY** **Section A: Averages & Range** 1. 18 2. 14 (Order: 7, 9, 12, 13, 15) 3. 4 4. 11 5. 15 (Total=120, Known total=105) 6. 41 (Order: 35,38,39,41,42,45,47) 7. 32 8. 5,5,5,9 (or other combinations) 9. 9,11,13 (or 10,11,14 etc.) 10. 25 (New total=85, Old total=60) **Section B: Bar Charts** 11. 12 12. 15 (10+5) 13. 56 (8+12+10+10+5+3+2+6) 14. 12 (20-8) 15. 14 (56÷4) 16. Wednesday 17. 210 18. 42 19. 35 (60-25) 20. 120 **Section C: Pictograms** 21. 16 22. 8 (12-4) 23. 40 (12+16+8+4) 24. 10 25. 4 (8 new votes = 2 symbols, +2 existing = 4) 26. 21 27. 15 28. 20 29. 2/5 30. 44 **Section D: Pie Charts** 31. 45° 32. 60 (90/360=1/4, so 15×4=60) 33. 6 (120°=24 people, so 30°=6) 34. 7.5° (360/48) 35. 45° 36. 5/18 (100/360) 37. 25 (150/360 × 60) 38. 24 (288/72=4, 4×6=24) 39. 60° (360/6) 40. No, sum is 360° but 5+85+90+100+80=360° → Actually Yes, it is possible. The sum is correct. **Section E: Line Graphs** 41. 7cm 42. Weeks 2-3 (3cm growth) 43. 6.8cm (34/5) 44. 10cm (12-2) 45. 15cm (consistent +3cm) 46. 14°C 47. 11am 48. 11°C (16-5) 49. 3pm-5pm 50. 11°C (16-5) **Fictional "Previous Year Paper"** 1. 623 2. 22 3. 5/8 4. 51 5. 14 6. £6.00 7. 34cm 8. 60cm² 9. 7 10. 36 11. 1h43m 12. 3:4 13. £18, £27 14. 36 15. 156 16. 5 (1,2,3,7,8,9) 17. 7 18. 28 19. 1/4 20. £5 21. 5 22. 21 23. 6 24. 81cm² 25. 56 26. 5 27. 10 28. 500g 29. 21:20 30. 1/2 31. £34 32. 80% 33. 5 34. 70° 35. 40p 36. 250km 37. 9 38. 4cm 39. 1 3/20 or 23/20 40. 5060 41. 1/2 42. 3/10 43. 0.15 44. 72 45. 8km 46. £384 47. 3/10 48. 30 49. 9.59 50. 36 **50 More GL Style Questions** 51. 12 52. 42.5mm 53. 15 54. 30 55. 8°C 56. 22 57. 4 58. 6 59. 20 60. 10 61. 8 62. 60° 63. £137.50 64. 10 65. 5 66. 15 67. 85 68. 28.33 69. 22.5 70. True 71. 70 72. 36 73. 16.5 74. 1 75. 23 76. Gym 77. 3 78. 9 79. 10 80. 20 81. 27 82. 24 83. 20 84. 4 85. 12.5 86. 1/2 87. Constant/Stayed the same 88. 24 89. 4 90. 5 and 3 91. 10 92. "Favourite Fruit" 93. 40 94. 4 95. 10 96. Yes 97. 17.5 98. 7 99. 0 100. Interpretation/Calculation from data Good luck!
