This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the questions: 1.1.1 Step 1: List the petrol prices from 2006 to 2016 and identify the frequency of each price. The petrol prices are: R7.04, R7.01, R10.40, R7.69, R8.17, R10.40, R11.04, R13.55, R14.33, R13.26, R12.35. R10.40 appears twice, while all other prices appear once. Step 2: Determine the mode. The mode is the value that appears most frequently. The mode of the price of petrol is R10.40. 1.1.2 Step 1: List the diesel prices from 2006 to 2016 and identify the frequency of each price. The diesel prices are: R6.54, R6.51, R11.27, R6.65, R7.38, R9.30, R10.25, R12.48, R11.80, R10.96, R12.35. Each price appears only once. Step 2: Determine the mode. Since all values appear with the same frequency (once), there is no mode for the diesel prices. The mode of the price of diesel is No mode. 1.1.3 Step 1: Sum all the petrol prices. Sum = 7.04 + 7.01 + 10.40 + 7.69 + 8.17 + 10.40 + 11.04 + 13.55 + 14.33 + 13.26 + 12.35 = 115.24 Step 2: Count the number of petrol prices. There are 11 prices (from 2006 to 2016). Step 3: Calculate the mean (average) price. Mean = SumNumber of prices = (115.24)/(11) ≈ 10.47636 Rounding to two decimal places for currency: The mean price of petrol is R10.48. 1.1.4 Step 1: Calculate the reduction in petrol price between 2014 and 2015. Petrol price in 2014 = R14.33 Petrol price in 2015 = R13.26 Petrol reduction = 14.33 - 13.26 = R1.07 Step 2: Calculate the reduction in diesel price between 2014 and 2015. Diesel price in 2014 = R11.80 Diesel price in 2015 = R10.96 Diesel reduction = 11.80 - 10.96 = R0.84 Step 3: Compare the reductions. Since R1.07 > R0.84, petrol showed a greater reduction. Petrol showed a greater reduction. 1.1.5 Step 1: Determine the range of petrol prices. Petrol prices: R7.04, R7.01, R10.40, R7.69, R8.17, R10.40, R11.04, R13.55, R14.33, R13.26, R12.35. Minimum petrol price = R7.01 Maximum petrol price = R14.33 Range of petrol = 14.33 - 7.01 = R7.32 Step 2: Determine the range of diesel prices. Diesel prices: R6.54, R6.51, R11.27, R6.65, R7.38, R9.30, R10.25, R12.48, R11.80, R10.96, R12.35. Minimum diesel price = R6.51 Maximum diesel price = R12.48 Range of diesel = 12.48 - 6.51 = R5.97 Step 3: Calculate the difference between the ranges. Difference = Range of petrol - Range of diesel = 7.32 - 5.97 = R1.35 The difference between the ranges is R1.35. 1.1.6 Step 1: Find the median of petrol prices. Order the petrol prices: R7.01, R7.04, R7.69, R8.17, R10.40, R10.40, R11.04, R12.35, R13.26, R13.55, R14.33. There are 11 prices, so the median is the (11+1)/(2) = 6^th value. Median petrol price = R10.40. Step 2: Find the median of diesel prices. Order the diesel prices: R6.51, R6.54, R6.65, R7.38, R9.30, R10.25, R10.96, R11.27, R11.80, R12.35, R12.48. There are 11 prices, so the median is the (11+1)/(2) = 6^th value. Median diesel price = R10.25. Step 3: Calculate the difference between the medians. Difference = Median petrol - Median diesel = 10.40 - 10.25 = R0.15 The difference between the medians is R0.15. Send me the next one 📸