Questions & Answers

Question 1 The editor of a UK college magazine is checking the latest edition of the magazine before it goes to print, but they have found some problems. (a) Three stories each have a piece of data missing. The topics of the three stories are: Story 1: A science project to find the fastest reaction time when mixing certain chemicals. Story 2: An interview with the winner of the inter-collegiate 1500 metre race. Story 3: The results of a survey to find the average time it took students to travel from their home to the entrance of the college campus. The three pieces of data are: A: 5 minutes 33 seconds B: 42 minutes C: 31.4567 seconds Match each story with the most appropriate piece of data, justifying your answer. (b) A story about the campus shop says that students spend on average £4.5682351 per visit. The editor rightfully thinks that this level of accuracy is unjustified. Round £4.5682351 to an appropriate level of accuracy, justifying your answer. (c) The word counts for the main articles in the latest magazine edition are: 220, 470, 1300, 250, 1100, 540, 380, 670. (i) Calculate by hand the median word count. Show your working. (ii) Calculate by hand the range of word counts. Show your working.

Question 2 A biologist is studying the development of a small population of rabbits. The length of each rabbit is recorded at the age of 3 weeks old and again at the age of 6 weeks old. The Minitab worksheet rabbits.mwx contains two columns. The column 3 weeks gives the length of each rabbit in millimetres at 3 weeks old and the column 6 weeks gives the corresponding length of the same rabbit in millimetres at 6 weeks old. Run Minitab and open this worksheet.

Question 3 The Office for National Statistics publishes the average price per litre in pence of ultra low sulphur/unleaded petrol ( The Minitab worksheet petrol.mwx contains the data for 2021 and has two columns. The column month gives the survey month where January is month 1. The column price2021 gives the average price in pence per litre in the year 2021.

Question 4 A group of 20 Open University students completed a practice quiz. The results for their first attempt were recorded and are represented in the following stemplot:

Question 5 A garden centre selling spring bulbs places a bulk order with their supplier each autumn for the following year's requirements of daffodil and tulip bulbs. The data for 2020 and 2021 are displayed in Table 1. (a) Calculate the overall spring bulb price ratio for 2021 relative to 2020. Round your answer to three decimal places. (b) Calculate the value of the spring bulb price index for 2021, taking 2020 as the base year. Round your answer to one decimal place.

Question 6 The Office for National Statistics publishes the Retail Price Index (RPI) and related data ( Price ratios and weights from the year 2020 are listed in Table 2. (The base date was January 1987.) (a) Why are pensioner households and high-income households excluded from the RPI? Justify your answer. (b) By considering the price ratio for 'Food and catering' in Table 2, comment on whether the food and catering prices in November 2020 have increased or decreased relative to January 2020. Justify your answer. (You do not need to calculate the percentage change.) (c) Using the data given in Table 2 (i) Show that the unrounded all-item price ratio for November 2020 relative to January 2020 is 1.009953. (ii) The value of the RPI in January 2020 was 290.6. Using the all-item price ratio given above in part (i), find the value of the RPI in November 2020 rounded to one decimal place. (d) An RPI index-linked pension was £733 per month in January 2020. The value of the RPI in January 2021 was 294.6. How much should the pension be per month in January 2021? Please give your answer rounded to the nearest pound. (e) Using relevant values of the RPI, calculate the purchasing power of the pound in January 2021 compared with the base date January 1987. Please give your answer rounded to the nearest penny.

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