The amount of water in each fruit has been correctly determined and technically there is nothing wrong with these results. It is clear to see that the watermelon contained the most water, while the peach contained the least water. However, because their starting weights were different it is less easy to tell which of the three fruits contained the largest proportion of water, which is the number that would actually help us understand the results best.This week is all about learning how to talk about numbers, and how to present them in a way that makes the meaning and implication clear. You will be shown how our scientist’s results can be presented in ways that make sense. The topics in this week are all tools to help convert numbers into a more useful and meaningful format.All of the topics covered are widely used and have applications in both everyday life and in further scientific study.As you work through this week, think about where you may have used these techniques or seen numbers presented in these ways. Did you realise what the numbers meant or how they were obtained? Think about where these techniques could be useful and whether you would now be more confident using them.3.2 RoundingSo far in this course, we’ve used terms such as ‘almost’, ‘about’ and ’around’ to describe numbers. They’re approximations, or estimates, which have been simplified, or ‘rounded’, sometimes to the nearest whole number, or sometimes to the nearest 10, or 0.1, in order to report the number appropriately. This is one of the main ways scientists communicate the level of confidence in a number’s accuracy.For example, if you took out a tape measure and measured the size of the room discussed in Week 2 as 3.1 m × 4.1 m × 1.9 m, the volume would be 24.149 m^{3}. But would you really be confident you knew the size of the room to within 0.001 m^{3}? The tape measure may not have been marked off in very small units, so your measurements may have been to the nearest 10 cm instead, but multiplying numbers tends to increase the number of digits. If you wanted to communicate your confidence in the final number, a more appropriate answer would be 24.1 m^{3} or even 24 m^{3}. Both of these figures are approximations rounded in two different ways, the first was rounded to ‘numbers after the decimal place’, the second was rounded to a number of ‘significant figures’. Both are valid approaches, and they reflect the level of confidence in the final answer. The next section discusses rounding to decimal places.3.2.1 Rounding to decimal placesOften when you use your calculator to do calculations, you will obtain an answer with many numbers following the decimal point. The numbers after the decimal point are referred to as decimal places. For example, consider the number 155.76403. There are five numbers after the decimal point, so you would say the number is given to ‘five decimal places’. The number of decimal places you see may depend on your calculator, although usually calculators can show at least seven decimal places.Although it may be tempting to give this entire number as your answer, it may not reflect its real accuracy, so the number needs to be rounded. This also makes the number easier to read, write and understand.When rounding a number, you need to decide to how many decimal places you are confident in your answer. If you are confident of the answer to two decimal places, you would round to 155.76. Before you discard the rest of the numbers, you need to work out whether to round the final digit up or down. If the first digit that you intend to discard is a 0, 1, 2, 3 or 4 then you can go ahead and discard them. If the first digit that you intend to discard is a 5, 6, 7, 8 or 9, then you have to increase your final digit by one. For example, if the number 155.76403 is to be rounded to one decimal place, you must look at the second decimal place, which is a six, and then round the first decimal place up by one, so the answer is 155.8Earlier in this week, you were introduced to an experiment to find the water content of different fruits. The initial weight of each fruit was measured in grams and presented to three decimal places with the watermelon weighing 160.156 grams, the cucumber weighing 127.751 grams and the peach weighing 64.375 grams.If you were working with these fruits in a recipe, for example, it might be more appropriate to report the weights as whole numbers, with no decimal places. So, in this example, the first decimal place immediately follows our chosen cut off, and is the value we use to round our answer. For the watermelon it’s a 1, for the cucumber it’s a 7 and for the peach it’s a 3.Only the cucumber has a first decimal place with a value over 5, so the last remaining digit needs to be rounded up. As for the watermelon and the peach, their numbers are less than 5, so they aren’t rounded up. The weights of these three fruits can therefore be written as 160, 128 and 64 grams.Last week, we calculated that 361,648,138 km^{2} of the Earth’s surface is covered by oceans. To simplify things we rounded this number to 361,650,000. Hopefully you can now understand how we obtained this rounded number. The next section covers rounding to significant figures, which is more commonly seen in science.3.3 Can you eat sig figs?The last section discussed rounding to decimal places, one of the ways in which scientists communicate their level of confidence or the precision of a number. In this section you will look at rounding to significant figures. While both approaches are valid, rounding to significant figures is a more common approach in science.The word significant means having meaning, and the significance of an individual digit within a number depends on its position. For example, the initial weight of the peach presented earlier was 64.375 g. This number has been presented to 5 significant figures. The 6 at the beginning of the number is the most significant figure because it tells you that the number is sixty-something. It then follows that the 4 is the next significant figure, and so on until all the digits are accounted for.Zeros are also important because their significance varies depending on their position in the number. For example, a raindrop has a volume of 0.034 cm^{3}. Despite the first two zeros, the most significant digit in this number is actually the 3. So here, where zeros are at the start of a number, they are largely ignored. In contrast, following a twenty minute shower, a puddle may have a volume of 108.472 cm^{3}. Here, unsurprisingly, the most significant figure is the 1, however the zero is also a significant figure in this number and its presence doesn’t mean that all the digits to the right can be ignored. The same rules apply for zeros situated at the end of a number and can be used to indicate the confidence in the number. For example, if we really knew the volume of the raindrop to more decimal places, the number could be reported as 0.0340. This would indicate that we are confident of the volume to the fourth number after the decimal point.You can use the same rounding rules that were introduced previously to round a number to a specified number of significant figures. For example, if you rounded the weights of the three fruits presented in the earlier section to three significant figures, this is what your results would be:Table 2 The water content of different fruits to three significant figures

Fruit

Weight before (g)

Weight rounded to 3 sig figs (g)

Watermelon

160.156

160

Cucumber

127.751

128

Peach

64.375

64.4

Can you see how you would come to these figures? While rounding to a number of figures after the decimal produces slightly different results for rounding to sig figs, both are valid and reflect confidence in the result.You probably round things more often than you realise, most likely when you are shopping. Most people automatically round up (or down) the price of an item so that it is easier to remember or combine with other item prices. However, human perception isn’t always that accurate. You’ve probably seen prices carefully set to appear lower. For example, a new phone or a spectacular pair of shoes can look like a bargain if priced at £199, but don’t be fooled into thinking that it’s meaningfully less than £200.3.4 Fractions and PercentagesThis week, you’ve seen how you may need to manipulate the bare numbers you obtain from an experiment in order to put them into a more useful format. As you saw in the bottled water video in Week 1, fractions and percentages are often used to communicate numbers in print, online and other audio-visual media. These are two simple techniques that you can use to make numbers more meaningful and they are not difficult to use.FractionsFractions are something which spark fear in a great number of people, yet simple fractions like a half (½) or a quarter (¼) are used every day. Numerically these two fractions are telling you how many of something you have (top number, or numerator) out of the total (bottom number, or denominator). For example, one out of every two hospital beds around the world is estimated to be occupied by someone suffering from a water-related illness. Using a fraction here provides much more context than an absolute number of beds occupied by those suffering from water-related illnesses without knowing the total number of beds.Fractions do not need to be any more complicated than this. The thing that complicates fractions is that they are typically reported in their simplest form, meaning that they are converted such that their top and bottom numbers are as small as they can be while maintaining their proportions. This is so that they are easier to comprehend. For example, if a jar contained 900 sweets of which 300 were blue, this could be expressed as 300/900. Although this is correct, it’s common practice to reduce this to smaller numbers – otherwise known as ‘cancelling down’. In this example, both the top and bottom number can be dived by 300 resulting in the fraction ⅓ (called a ‘third’).Scientists rarely present their results as a fraction because they can be fiddly to reduce to their smallest parts, and even when this is achieved the bottom number may differ, making it more difficult to compare like with like. Instead scientists commonly write fractions out as decimal numbers or percentages to communicate numbers as a proportion of the whole.PercentagesTake our example from earlier, where the scientist measured the amount of water in three different fruits. Their results indicated that 160 g of watermelon contained 144 g of water, 128 g of cucumber contained 120 g of water and 64 g of peach contained 56 g of water. Note that these weights have been rounded to the nearest whole number.Percentages are calculated by dividing the number of parts you are interested in by the total number of parts available and multiplying the answer by 100. So, in the fruit example you might want to find out what percentage of the fruit is water. For a watermelon, you need to divide 144 by 160 and multiply the answer by 100. Try using your calculator to find the percentage. You should find the answer to be 90%.Activity 3.1 Calculating a percentageAllow about 5 minutesTry calculating the percentage of water contained in the cucumber and the peach. Which of the fruits has the highest percentage of water content?Percentages are not just used in science. You will have met percentages in other contexts – if you have received a 3% pay rise or seen an advert for a 20% off sale, for example. The same principles apply to these numbers as the fruit. For example, to calculate your pay following a 3% pay rise, you first calculate 3/100 of your income, and then add this result to your current annual income.You can also think of this as 103% of your current salary. To work this out using your calculator or smartphone, multiply your current salary by 1.03. (Remember, your base salary is 100%.)Some calculators and smartphones have a % button and you may have noticed that we haven’t used it during this section. That might seem a little odd but the reality is that we’re not sure that all % buttons operate consistently and we ultimately don’t understand how some of them work. As a result, it is far easier to simply ignore the existence of the % button entirely and just work out the percentage yourself.Finally, the really scary stuff is when you try to add, subtract, multiply and divide fractions. The honest truth is scientists just convert these to decimal numbers and use a calculator.3.5 Negative numbersnumbers_negative_final_platform The Celsius scale, also known as the centigrade scale, is commonly used to measure temperatures. The scale is based on the temperatures which control the physical state of water, with zero degrees Celsius being the temperature that ice melts. In other words, when water changes from a solid to a liquid state. And 100 degrees Celsius being the temperature at which water boils, and therefore changes into a gas state. However, the Celsius scale is not limited to this range. For example, the temperature of the Sun is about 5,500 degrees Celsius. And most home freezers are set to around minus 18 degrees Celsius. This means that the temperature of your freezer is 18 degrees less than zero. The range of temperatures of Earth varies greatly, from warm desert areas around the Equator, to frozen continents at the poles. The tourist, travelling to some iconic places around the globe, might experience temperatures like 10 degrees Celsius in London, England, minus five degrees Celsius at Niagara Falls in Canada, 40 degrees Celsius at the pyramids in Egypt, minus 30 degrees Celsius in Antarctica, and five degrees Celsius in Machu Picchu in Peru. Our tourist experienced a total range of 70 degrees Celsius during his trip, from minus 30 degrees in Antarctica to 40 degrees in Egypt. These temperatures are not even the hottest or coldest ever recorded on Earth. On the 10th of July, 1913, Furnace Creek in California reached a sweltering 57 degrees Celsius, making it the highest recorded temperature on Earth. And in August 2010, a satellite recorded that the temperature in Antarctica had reached a chilly minus 94.7 degrees Celsius.Intuitively you might consider zero as the lowest possible number, there can’t be anything less than nothing, right? Numbers below zero seem unnatural, or complicated to understand.The video uses temperature to illustrate that negative numbers are not uncommon and are used all the time. Negative numbers are written with a minus symbol in front of them. For example, a normal household freezer is often set to -18 ˚C (or 18 degrees below zero).Activity 3.2 Temperatures and negative numbersAllow about 15 minutesThere is a wide range of temperatures that might be experienced by visiting different countries. The temperatures of the five countries in the video were all different, with two below 0 ˚C. Post your response to these questions in the forum thread for this activity and discuss with your fellow students:How hot or cold does it get where you live?Where are the hottest and coldest places you’ve visited?Can you think of any other everyday situations where you use negative numbers?3.6 Week 3 quizCheck what you’ve learned this week by taking this end-of-week test.Week 3 quizOpen the quiz in a new window or tab then come back here when you’ve finished.3.7 Week 3 summaryYou’ve nearly made it through the course, and you’ve examined how you can present numbers as fractions or percentages and you’ve also considered when and why you should round numbers.Hopefully you enjoyed the video on negative numbers, and perhaps it gave you some ideas on where to go (or where to avoid) next time you start planning a holiday!Next week you’ll be looking at averages, correlation and interpreting graphs before taking the end-of-course quiz to see what you’ve learned.Go to Week 4.Week 4: Presenting numbersIntroductionWelcome to week four, the final week of Understanding numbers.Last week you covered some of the basics of presenting numbers so they make sense, like rounding and percentages. This week, you'll learn about graphs, plotting them and interpreting them.Graphs appear everywhere, and there is a reason for that. They’re often the key to understanding a science experiment or an issue, like changing rainfall patterns. A table of numbers can be difficult to decipher, but a graph tells the story visually, in a second. So you’ll spend quite a bit of this week looking at and plotting graphs.And finally, there’s the End-of-Course Test. Please have a go. It will remind you of the many topics that you've encountered in this course. So enjoy the last week, and good luck with the test.Your guide, Janet, is back to introduce Week 4 of Basic science: understanding numbers.4.1 How do people ‘get’ science numbers?Communicating science through numbers, particularly in the media, is often in the form of simple graphs. Scientists also communicate results in graphical form, so creating and interpreting graphs is a very important skill for a scientist.When you pick up a newspaper or magazine do you open it and immediately start reading, or do you flick through the pages, pausing at those with images that catch your eye to read those articles first?Consider the bottled water video from Week 1. It uses graphs, like the one below, to present science numbers. But is this really a graph or is it just a graphic intended to illustrate the doubling of the bottled water industry?Numbers are used in articles designed for the public, as well as being an invaluable tool for scientists, economists and many others, not just to present data, but to analyse data and identify patterns and trends.4.1.1 Using graphsMedia graphics and graphs come in many forms. This is a bar chart presenting the absolute numbers of children in families (not fractions or percentages). These charts can be drawn with the bar displayed either horizontally or vertically. When the bar extends horizontally, they may also be known as ‘row charts’ and when the bar extends vertically, they may be known as ‘column’ charts’.This is another type of graph (a pie chart) commonly used in media, categorising the average family’s expenditure on food and drink. Is it possible to judge whether your own family is similar? What further data do you need to help you do that?Time series graphs are also commonly used in the media. They can be used to identify a trend, and often imply some outcome in the future. For example, using this graph, who do you think won the UK election in 1997?Finally, some graphs cross the boundary between presentations for fellow scientists and those intended for public consumption in the media. The graph shows the range of global average temperature from 1860 to 2000. Why does the graph not extend further back in time than it does? What does the graph show overall? Is the flat zone between 1940 and 1960 important? Is the recent temperature rise faster and sustained? The line appears to flatten in the late 1990s – does this mean that global temperatures have plateaued?Pay attention to the news today, either on television, in papers or on the internet. How many visual graphical techniques do you notice? Think about whether these are good, bad or even dangerous.4.2 AveragesMany numbers presented in the media are averages, commonly used in statements like ‘the average temperature rise due to climate change since 1860 was 0.8 °C’, or ‘rainfall was 40% above average for June’. But what does ‘average rainfall’, or ‘average temperature’, actually mean?The word ‘average’ is often used to mean ‘ordinary’, ‘typical’ or ‘normal’. This is fine in everyday contexts, but, in scientific contexts, average also has a mathematical meaning. It is used to report the typical value within a set of data, sometimes with an associated range indicating the spread of the data. This makes averages useful when presenting data because, instead of describing each value in the dataset, you can present just one value which approximates your whole set.4.2.1 Types of averageThere are three main types of average: mean, median and mode. Each of these techniques works slightly differently and often results in slightly different typical values.The mean is the most commonly used average. To get the mean value, you add up all the values and divide this total by the number of values. For example, if you wanted to find the mean of 11, 14 and 17, you would add them to give a total of 42, then divide that by the number of values you have, which is 3. So the mean of 11, 14 and 17 is 42/3 = 14.The other types of average are:The median, which places all your values in order from smallest to highest and finds the one in the middle. For example, the median of the values 3, 3, 4, 5, 9, 11 and 16 is 5.The mode is the most commonly occurring value. For example, the modal value of 1, 3, 6, 6, 6, 6, 7, 7, 12, 14 and 24 is 6 because it appears the most times.4.2.2 Using averagesWhen the average of a dataset is presented to you, you need to consider which type of average has been used. Consider the average number of feet a person has. Most people in the world have two feet, so the modal value will be two. Similarly, if you were to use the median average, you would also find the answer to be two, as a very small minority of people have fewer than two feet, so two would remain the middle number.However, if you were to calculate the mean, you would find that the answer is no longer two. There are a minority of people with fewer than two feet, for a variety of reasons, but this is enough to reduce the mean ever so slightly. As a result, almost everyone has more than the mean number of feet.That’s enough about feet. Let’s instead consider the average of a scientific dataset. Average monthly rainfall is worked out from the recorded rainfall for that month over a specified number of years. The numbers below are the recorded January rainfall (in millimetres) for London, UK over 10 years. For simplicity these are arranged in order of smallest to highest.17, 19, 51, 56, 69, 72, 72, 74, 75, 77The data show that January rainfall has ranged from 17 mm to 77 mm in the ten years that this dataset covers. The mean average rainfall is 58 mm to 2 sig figs. Do you agree that the average rainfall should be reported to 2 sig figs?The median rainfall is the middle value in this list. Because there are an even number of years in the sample, there is not a single middle value. Instead, both 69 and 72 are the middle numbers. The median is calculated as the number midway between these two numbers and is therefore 71 mm to 2 sig figs. The mode is the most common value, which is 72 mm.This demonstrates perfectly the sensitivity of the mean average to extreme values. The mean average is lower than the median or mode averages due to the two very dry Januarys, which experienced only 17 and 19 mm of rain.You will return to average rainfalls later this week when you look at plotting and interpreting graphs.4.3 Types of graph and drawing graphsDrawing graphs and types of graphSPEAKER:Graphs are a simple and effective way of presenting numerical data. Such visual representationsenable usersto identify patterns easily, and are a powerful tool in illustrating the relationship between two quantities. Today, graphs are used almost everywhere, from news articles to television adverts, and we'll demonstrate how some common graph types are plotted.Line graphs have two axes, an x-axis, which goes across the page, and a y-axis, which is vertical. These are your reference lines which carry the scale of the graph, and help you to locate where to plot each piece of data. Scientists like consistency, and it's standard practice to put the thing you're measuring on the y-axis.For example, if you're interested in the amount of rainfall per day for five days, you'd put rainfall on the y-axis, and the number of days on the x-axis, making sure that you include the units that each axis is measured in. You'd plot each piece of data in turn, starting with the day, and then the rainfall. For example, the first point goes at the intersection between day one and 1.5 millimetres of rain, the second, at the intersection between day two and one millimetre of rain, and so on until all the points are in place. And because this is a line graph, consecutive points are then connected with a line. Bar graphs are similar in their structure, also having an x and a y-axis. Bar graphs are most commonly used to plot the frequency of something in specific categories. If we use the same data as the previous example, the day would be the category, plotted on the x-axis, and the rainfall represents frequency, which is plotted on the y-axis. This time, instead of the point of intersection, each day category has a bar or column, with its height reflecting the rainfall experienced on that day.The final type of graph, commonly presented in newspapers or during news articles on TV, are pie charts. Like bar graphs, these also use categorical information. They begin with a circle which is then divided into sectors, the size of which represents the relative size of each value. Once complete, your graph would look like this. To calculate the size of each sector, it's easiest to calculate each category's value as a percentage. However, these graphs are more difficult to plot 1 by hand than the other examples, and are often plotted on a computer which works out this step for you.The graphs you see in magazines, newspapers, or advertisements take many forms. However, they mostly revolve around the three basic graphs you've seen here. Next time you see a graph, think about which graph type it is. Could the information have been presented better in a different graph type?So, you’ve seen how the same data can be presented using different types of graph, but how will you decide which type of graph to use for a given situation?4.3.1 Interpreting graphsIt is often said that ‘a picture paints a thousand words’, but how many words can be painted by a graph? Once you know how to interpret graphs, they can be just as thought-provoking as a picture. This section uses bar graphs, line graphs and pie charts to assess how the monthly average rainfall for the United Kingdom varies throughout the year, and compares this with the same data for India. The data used here (from the Climatic Research Unit of the University of East Anglia) is a mean average for the years 1990 to 2009.Each of these graphs and charts can also be viewed on infogr.am. Infogr.am is designed for creating interactive infographics and is a quick and easy tool for plotting colourful and varied graphs and charts, which can then be saved and shared with others. You’ll get the opportunity to create your own graphs later in the week.Using graphs to view dataThis first graph is a bar chart of average rainfall per month in the UK. The height of each bar represents the average rainfall (in mm) in each month. The graph shows that, on average, the driest month in the UK is May, while October is the wettest month. You can also see the UK’s seasonal cycle, with the autumn and winter months (September–February) being wetter than the spring and summer months (March–August).Using graphs to compare dataTo compare the rainfall of the UK with that of India, you could plot the data for India on a bar chart and compare the two charts next to each other. However, a line graph plotted with one line for each country’s rainfall allows both to be compared on one graph.On this graph, the yellow line represents the average rainfall in the UK, while the red line represents the average rainfall in India. Between October and April in India, rainfall is on average lower than in the UK, but the summer months in India coincide with the Indian monsoon season, so these months are considerably wetter. Perhaps a graph like this might help you decide when and where to go on your next holiday!It is difficult to determine which country is wetter overall from the line graph. The UK is generally wet throughout, but India has such a dramatic monsoon season that it might counterbalance the drier months earlier in the year. Using a pie chart can illustrate this very effectively.The UK slice of the pie chart forms a greater proportion of the whole, meaning that on average the UK is wetter than India, although the difference between the two is perhaps less than you might have expected. In fact, this is one of the things that make them an interesting comparison, two countries, each with a very different climate but similar total rainfall. If you calculate each as a percentage, you can see that the UK makes up 55% of the graph, whereas India makes up the remaining 45%. This chart is a perfect example of how graphs can be used to mislead an audience – the rainfall of the UK and India are not dependent on one another.Interpreting graphsThis section is intended to help you on the way to interpreting different kinds of graph. The three main types of graph can provide lots of information and it’s worth spending a few minutes thinking through the implications and insights for each of them. Remember that the most important information is:the height of the columns in bar graphsthe x and y values for line graphthe proportion represented by each category for pie charts.Finally, scientists often have to read numbers from a graph, and this can be an important way to gather information. Look at this graph of the same Indian and UK rainfall data with the data point markers removed, and the curves smoothed. Smoothing is quite commonly used to emphasise trends in data. However it also has the potential to be misleading.In this graph, without the clear data markers indicating monthly values, the graph appears to show an almost continuous set of rainfall measurements. Compare the highest rainfall value for India on this graph and the previous one. To do this, identify the highest point on the curve and read the monthly value on the bottom axis and the rainfall value on the side axis.Both the date and the peak rainfall value appear to be different in the two graphs even though they are based on the same data. On the first graph, the peak rainfall value for India was 255 mm in July, but on the smoothed curve without markers, the peak rainfall appears to be around 265 mm sometime in the first half of July. Is this second interpretation correct? Or are there lessons to be learned about interpreting line graphs of scientific data?4.4 Correlation, causation and coincidenceGraphs are a great tool for presenting complicated results: they can help communicate the relationship between two or more variables.CorrelationA striking example of this is the recognition of a correlation between smokers and lung cancer patients. Lung cancer used to be a rare disease, with only 1% of autopsies performed by the Institute of Pathology of the University of Dresden in 1878 showing malignant lung tumours. Unfortunately, lung cancer did not remain rare and, over the following 50 years, this figure rose to more than 14%.CausationA particularly observant scientist, Franz Müller from Cologne Hospital, published a study in 1939, identifying the correlation between tobacco smoke and lung cancer. The study compared 86 lung cancer cases and a similar number of cancer-free controls, showing that the people who smoked were far more likely to suffer lung cancer.However, while a correlation between two sets of observations or measurements can point to a causal relationship between them, correlation does not always imply causation. This was part of the basis for the long running debate about smoking and lung cancer, but it was some decades later before this link was accepted following the emergence of scientific evidence for the cause.CoincidenceConsider this odd correlation between worldwide launches of non-commercial space missions and the number of sociology doctorates awarded in the USA. The graph shows how both of these variables rise and fall together, as if connected in some way. You might wonder if the sociology graduates work on the space missions? However, this is not the case, with sociology doctorates usually working in the field that they are actually trained in and not turning their hands to physics or space engineering. This correlation, as real as it is, is a coincidence. It is also not a freak occurrence; a quick internet search of ‘spurious correlations’ will bring up a whole host of correlations that are purely coincidental.The role of a scientist is to critically assess correlations encountered in their results. There are several criteria scientists use to test the validity of correlations and their significance. The detail is beyond the scope of this course, but they are a crucial science skill. Ways of testing correlations include the goodness of fit, in other words, working out how good the correlation is, and whether it can be reproduced and examined further.What about the apparent correlation in the graph of space missions and sociology graduates? A scientist might ask why the graph is only plotted between the years 1997 and 2009, since both space missions and sociology graduates were around before and after those dates – did the person plotting the data avoid those earlier and later dates because the correlation breaks down?Despite the precaution such as goodness of fit and reproducibility, sometimes scientists get it wrong and over interpret a correlation or apply causal mechanisms to coincidences. Can you think of any examples where this has been the case?4.5 Create and share your own graphAs a scientist, it is important both to be able to present numbers clearly and in a way which emphasises the significant results, and to interpret graphs to extract the essential data. This week, you’ve concentrated on how science numbers are presented, focusing on bar graphs, pie charts and line graphs. In this section, you should take the opportunity to make your own graphs. You will have the opportunity to share and discuss them in the next section.Activity 4.1 Your own graphAllow about 30 minutesPart 1 Creating your graphDownload the Rainfall data and the Instructions for Infogr.am.Use the data to plot different kinds of rainfall graphs for a range of countries over the period 1990–2009. Think carefully about which type of graph will best demonstrate your results.We recommend that you use infogr.am, which is designed for creating interactive infographics. It is a quick and easy tool for plotting colourful and varied graphs and charts which can then be saved and shared with others. The site is free to use – you do not need to register for any paid-for premium account.If you prefer you may also plot your graphs by hand or by using a program like Excel or Google Sheets and share a photo via social media (don’t forget to use the course hashtag #OLSciNum).We plotted the rainfall in Spain and Australia, because both are relatively dry but in opposite hemispheres of the world, so would they have similar or different patterns?In fact, as you can see from the plot, both countries are dry and wet in the same annual pattern despite being in different hemispheres. While Spain had the pattern we expected, dry in summer and wet in winter, Australia appears to be dry in the winter and wet in the summer.Part 2 Sharing your graphGo to the forum thread for this activity and share the graph you created, either as a link to an infogr.am or a link to an image shared via social media or via an image hosting site.Do the countries you are comparing have similar rainfall or are they very different? What time of year would you choose to visit those countries? Discuss these points with your fellow students.4.6 End-of-course quizCheck what you’ve learned during the course by taking this End-of-course quiz.End-of-course quizOpen the quiz in a new window or tab then come back here when you’ve finished.4.7 Congratulations – you’re a scientist!Well done for completing this four-week course on understanding numbers! Over the past four weeks you’ve looked at how scientists:communicate with each othercalculate area, volume and density and what this means for the Greenland ice sheetpresent numbers using significant figures, decimal places, fractions and percentagesuse different types of averages, draw and interpret graphs and find correlations in data.If you would like to take your study of science further, why not take the sister course, Basic science: understanding experiments. It will help you think like a scientist by carrying out experiments at home and making your own observations.We’ve also created an area to enable you to take your study of numbers in science further.We would love to know what you thought of the course and what you plan to do next. Whether you studied every week, dipped in and out or jumped straight to the conclusion, please take our Open University end-of-course survey. Your feedback is anonymous but will have massive value to us in improving what we deliver.Return to course progress pageWeek 1Sagan, C. (1990), 'Why We Need To Understand Science', Skeptical Inquirer, vol. 14, no. 3 [Online]. Available from http://www.csicop.org/si/show/why_we_need_to_understand_science. Accessed 12 October 2015.This course was written by Leanne Gunn, Sion Hughes and Simon Kelley.Except for third party materials and otherwise stated in the acknowledgements section, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence.Every effort has been made to contact copyright owners. If any have been inadvertently overlooked, the publishers will be pleased to make the necessary arrangements at the first opportunity.Don't miss out:1. Join over 200,000 students, currently studying with The Open University – http://www.open.ac.uk/choose/ou/open-content2. Enjoyed this? Find out more about this topic or browse all our free course materials on OpenLearn – http://www.open.edu/openlearn/3. Outside the UK? We have students in over a hundred countries studying online qualifications – http://www.openuniversity.edu/ – including an MBA at our triple accredited Business School.