Calculate, plot, draw, complete and predict: the data command words

The river gauge at Talonford, a city in the fictional land of Owlobia, reads three point two metres. How long before the water reaches the top of the flood wall? The level is rising by nought point two metres every hour. The flood wall along the high street holds back water up to four point nought metres. The council has to decide now whether to clear the street or wait. Nobody needs an essay here, because the decision rests on one calculation and one prediction, and both have to be right. The answer comes once the routine for data questions is in place.

Calculate means find a value from the figures you are given, and sometimes the word is missing, as in a question that asks what is the total. Every calculation runs the same routine of four steps. Step one, read which calculation is asked: mean, median, range, total, percentage or percentage change. Step two, pick the figures the question names, such as one month, two years or three sites. Step three, write the method down. Step four, give the unit and round the way the question says. Which step stops you using every month, when the question names only one? The second one. Each step guards against a slip like that, and written working is a safety net, because if the final figure goes wrong, the working can still show the right method. One rule before the first sum. The range is the highest value take away the lowest value, wherever they sit in a table. A weather station in Owlobia recorded a week of daily rainfall, in millimetres. Monday four, Tuesday nought, Wednesday twelve, Thursday seven, Friday twenty-one, Saturday three, and Sunday ten. The first question on that table asks you to calculate the range. What is the range of that week's rainfall? The highest is twenty-one, on Friday, and the lowest is nought, on Tuesday. Twenty-one take away nought is twenty-one millimetres. The trap is the first and last in the table. Sunday take away Monday is ten take away four, which gives six, and that is not the range. One examiner's report on a range question records the good news first: "Most candidates were given 2 marks for this calculation, recognising they needed to subtract the lowest from the highest to be successful." On the same question, it adds: "Fewer candidates selected the first figure listed in the table and the last figure listed in the table, which was incorrect." The habit is to ring the highest and the lowest before you subtract. Now a different calculation on the same week. Calculate the mean daily rainfall, and give your answer to one decimal place. The mean is the total divided by how many values there are. Try it on paper: the total, then the division, then the rounding. The total first. Four, add nought, add twelve, add seven, add twenty-one, add three, add ten, gives fifty-seven millimetres. Then divide by the seven days. Fifty-seven divided by seven is eight point one four two, and the digits run on. Last, the rounding. One decimal place keeps the eight point one, and the next digit is a four, which is less than five, so it stays eight point one millimetres. Eight point one four ignores the instruction, and eight on its own has too few places. One examiner's report on a percentage question says: "Those that dropped marks either failed to answer as a whole number as requested and instead gave answers to 1 or 2dp." The fix is to underline the rounding instruction and round only at the very end. Steps one and two catch the other slips. One examiner's report says that some students were "calculating the mean instead of the median", and another says: "The most common error candidates made was to calculate the mean for all six values for the east and west of the groyne." Circling the word and the figures named is the habit that stops both.

Percentage change runs the same routine, and this time the first three steps are done for you. Marksby's population was forty-eight thousand in twenty eleven and fifty-five thousand five hundred in twenty twenty-one. The question asks for the percentage increase, as a whole number. The increase is fifty-five thousand five hundred take away forty-eight thousand, which is seven thousand five hundred. Divide that by the starting figure, forty-eight thousand, which gives nought point one five six two five. Multiply that by a hundred, which gives fifteen point six two five per cent. What is fifteen point six two five per cent as a whole number, and why? Sixteen per cent. The digit after the fifteen is a six, which is five or more, so fifteen rounds up to sixteen. Three other answers each skip a step. Nought point one six forgot to multiply by a hundred. Fifteen point six ignored the whole number. Thirteen point five divided by the new population instead of the starting one. One more check belongs at the very start of the routine: look at the units. If the figures are already percentages, adding them already gives a percentage, and no extra step is needed.

Draw, plot and complete ask you to add data to a graph, a map or a table accurately. Plot each value exactly where it belongs, with a ruler and a sharp pencil, and match the style already there: the same bar width, the same shading, the same kind of cross. A cliff on the Barnwing Coast has been measured since two thousand. Its total retreat was four metres by twenty oh five, nine by twenty ten, thirteen by twenty fifteen, and eighteen by twenty twenty. The first three values are plotted, with a best-fit line through all four, and the question asks you to complete the graph by plotting the last one. What do you check on the graph before you mark that cross? The scale on the upright axis. Here each step is five metres, so you find twenty twenty along the bottom, count up to eighteen metres, just under the twenty mark, and mark a neat cross that matches the others. Accuracy is what this task tests. One examiner's report on a plotting question notes: "There was a small but significant group that did not receive the mark because they lacked accuracy in plotting the information." The fix is to work out what one small square is worth, then plot with a ruler and a sharp pencil. Leaving it blank is the other risk. One examiner's report on a graph to complete says: "This was not entirely successful, as many failed to complete this straightforward task." That came even after the instruction was printed above the graph. The habit is to scan every figure in the paper for something to plot or finish.

Make a prediction means use the evidence to judge what will happen next, and on a graph, that means extending the trend line and reading the value off it. The second part of the cliff question asks you to use the best-fit line to predict the total retreat by twenty thirty. How do you read the twenty thirty value off the best-fit line? Extend the best-fit line with a ruler to twenty thirty, then read straight across to the upright axis. It gives about twenty-seven metres, and the value must come from your own line. A rough check agrees. The cliff retreated fourteen metres in the fifteen years from twenty oh five to twenty twenty, which is about four point seven metres every five years. Two more of those on top of eighteen gives about twenty-seven. One examiner's report on this kind of question describes answers that went wrong by "either misdrawing the line despite getting this question correct or drawing the line correctly but then providing the incorrect answer to this question." The fix is to draw the read-off line on the graph and copy its value. A prediction holds only if the trend continues, so say that in the answer. A storm season or new sea defences could change the line. Now back to the gauge at Talonford, with the routine in hand. From three point two metres to a four point nought metre wall, at nought point two an hour: how many hours? Step one, two sums: a take away for the gap, then a divide for the time. Four point nought take away three point two is nought point eight metres of room left. Then nought point eight metres divided by nought point two metres an hour is four hours. That is a prediction too, because it holds only if the river keeps rising at the same rate.

Through the routine once more, and you go first on each.

What are the four steps of the calculate routine? Which calculation, which figures, the method written down, then the unit and the rounding asked for.

Now new figures: six, fifteen, two, eleven and nine. What is the range? Thirteen. The highest is fifteen and the lowest is two, so fifteen take away two is thirteen, and the first and last values play no part.

Now rounding: what is twenty-three point four six to one decimal place? Twenty-three point five. The next digit after the four is a six, which is five or more, so the four rounds up to five.

Now prediction: what must a predicted value agree with? Your own best-fit line, extended and read off, and it holds only if the trend continues.

The council at Talonford gets its answer from a take away and a divide: the water reaches the top of the wall in four hours, if the river keeps rising at the same rate. One calculation and one prediction, both run through the same routine. That wraps up the short-answer command words.

If you're solid on this, give it a thumbs-up. If the routine is still wobbly, save it, and rewatching only the worked examples is enough to bring it back.

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