1. Revision lecture

2. Q1 – Q3 Q1. What is 20% of £140? Q2. What percentage of £20 is £3? Q3. How much would 12 DVDs cost at £5 each plus 20% VAT? = (20/100) × 140 = 28 3/20 expressed as a percentage = (3/20) × 100 = 15% = (12 × 5) × 1.20 = £72

3. Q4 Q4. A manufacturing company sets the sale prices of its items so that the raw material costs are 40% of the sales price. If the raw materials for an item cost £30, what will the sales price be? Raw materials r, sales price s r = (40/100) × s s = (100/40) × r s = (100/40) × 30 s = £75

4. Q5 – Q6 Q5. A call centre measures the length of time that each caller has to wait until their call is answered. What type of data is this? Q6. In an online survey of the service provided by a hotel, customers are asked to rate the service as either: excellent, good, average, poor, very poor. What type of variable is the service rating? Numbers with a unit so: quantitative Can take any value over 0 so: continuous Categorical and ordinal

5. Q7 Q7. A retail store collected data on the colours of plain polo shirts purchased by customers. They recorded data using the numbers 1 to 5 as follows: 1 = white, 2 = blue, 3 = green, 4 = red, 5 = black. Which measures of the centre of data make sense for this data? Categorical nominal data Only the mode makes sense

6. Q8 Q8. A student was asked to estimate the average engine capacity of all motor vehicles in the UK. She therefore visited a large city centre car park near her home and wrote down the engine capacity of every tenth car in the car park. The total number of observations obtained was 50. All except one of the following could cause bias in her sample. Which could not be a cause of bias? A: The city's inhabitants may be richer than average B: Lorries are not allowed in that car park C: The sample size is very small compared to the total population D: The car park is the most expensive in the city E: She took her sample at about 10 p.m. Small sample causes uncertainty, not bias

7. Q9 – Q10 Q9 – Q11 A supermarket counted the number of items bought by customers. The number of items bought by each of the first 6 customers were: 10, 25, 4, 12, 7, 14. Use this data to answer questions 9-11: Q9. The mean number of items is (to 1 decimal place) Q10. The median number of items is (to 1 decimal place): Mean = (10+25+4+12+7+14)/6 = 12 Put data in order: 4, 7, 10, 12, 14, 25 Median = (10 + 12) / 2 = 11

8. Q11 Q9 – Q11 A supermarket counted the number of items bought by customers. The number of items bought by each of the first 6 customers were: 10, 25, 4, 12, 7, 14. Use this data to answer questions 9-11: Q11. The range of the number of items is: Range = max – min = 25 – 4 = 21

9. Q12 Q12. Which one of the following is the best description of what the standard deviation measures? A: The centre of the data B: The range of the data C: The typical variation of the middle half of the data D: The typical variation of all the data E: The linearity of the data

10. Q13 Q13 – Q15. The following table shows the number of different types of cars sold by a garage in 2010 and 2011: Q13. The percentage change in the number of sports cars sold from 2010 to 2011 was (to the nearest percent): 2010: 114 Change = 82 – 114 = –32 % change = –32 / 114 = –28%

11. Q14 Q14. The percentage of family cars sold in 2011 out of the total cars sold in 2011 was (to the nearest percent): Total for 2011 = 305+294+155+82 = 836 Family % = (294/836) × 100 = 35%

12. Q15 Q15. The garage has decided to draw two charts of the data for 2011. It wants chart 1 to show clearly the differences in sales for the types of car. It wants chart 2 to show clearly the proportion out of the total sales for each type of car. Which one of the following would be the best choice of charts to use? A: Chart 1: bar chart. Chart 2: pie chart B: Chart 1: histogram. Chart 2: pie chart C: Chart 1: pie chart. Chart 2: bar chart D: Chart 1: pie chart. Chart 2: histogram E: Chart 1: histogram. Chart 2: bar chart

13. Q15 Bar chart emphasises difference in sales

14. Q15 Pie chart emphasises proportions Hence: answer A

15. Q16 Q16. A call centre recorded the length of time that callers had to wait for a sample of phone calls. The data is summarised in the following table: The call centre then drew a histogram of this data. Note that the last category of 120-180 is wider than the other categories. Twice as wide: Plot at height 2

16. Q16

17. Q17 The above stacked column chart shows the monthly project costs for an IT project split into three categories: system design, equipment, and installation. What percentage of the total costs were equipment costs? Total costs = 40+50+30=120 Equipment = 0+20+10 = 30 Percentage = 30/120 × 100 = 25%

18. Q18 Q18. An Excel spreadsheet has the number of items sold in cell B2 and the sales price in cell C2. The user of the spreadsheet wants to calculate the number of items multiplied by the sales price and put the answer in cell D2. What Excel formula should be used in cell D2? A: =B2xC2 B: =B2*C2 C: B2xC2 D: B2*C2 E: B2^C2

19. Q19 Q19. An Excel spreadsheet has the following formula in cell C2: =B2/$B$6. This formula is then copied to cell C3. What will the formula be in cell C3? A: =B2/$B$6 B: =B2/$B$7 C: =B2/$C$6 D: =B3/$B$6 E: =B3/$B$7