Plotting and reading graphs

A rechargeable bike light's box says up to five hours. You set off on full beam, and the low-battery warning starts flashing after four. The box did not lie. A graph on the light's data sheet showed exactly when the warning would come, for anyone who could read it.

Graphs need nothing from the other videos in this set, though the charts video sits right beside this one.

A line graph shows how one measured quantity changes as another one changes. The first choice is which quantity goes on which axis. A student tests a six hundred millimetre pine shelf, hanging loads from its middle and measuring how far it sags. Load is measured in newtons, the unit of force. At nought newtons there is no sag. At twenty newtons the sag is one point five millimetres, at forty it is three point one, at sixty four point four, at eighty six point nought, and at a hundred newtons seven point six. Which goes across the bottom, the load or the sag, and why? The load. The student chose it and set it, and the sag is what came out. What you set goes across, and what you measure goes up. Next, the scale. Count in steps of one, two, five or ten, so every square is worth the same. The loads reach a hundred, so across counts in tens. The sag reaches seven point six, so up counts in ones, from nought to eight. Each axis gets its title with its unit: load in newtons, sag in millimetres. An uneven scale, steps of ten and then twenty-five, bends the shape of the data. A scale that only fills one corner of the grid hides it. Spread the data across most of the grid. Plot each pair with a small cross: across first to the load, then up to the sag. The crosses lie close to a straight line through nought, nought. So rule one line of best fit through the middle of them, with crosses either side of it. It passes close to a hundred newtons and seven point six millimetres. Why rule one line through the crosses instead of joining them dot to dot? Every test reading carries a small error. One line follows the trend of all six, which evens those errors out. This is a skill that tends to go well. One examiner's report records: most candidates successfully constructed and labelled the line graph. The habit behind that is the one here: titles with units, an even scale, then crosses and a ruled line.

Now reading values back off the graph. Go from the value you know to the line, then across or down to the other axis, and say the answer with its unit. Using the line, what is the sag at seventy newtons? About five point three millimetres. Up from seventy to the line, then across. A dot-to-dot version only uses the two nearest readings, and gives about five point two. The line of best fit uses all six readings, which is why it is the one to read. Graphs read backwards too. The shelf's specification says it must sag no more than five millimetres. Up to what load does the shelf meet that five millimetre limit? About sixty-six newtons. Across from five millimetres to the line, then down. A careful reading lands between sixty-four and sixty-seven. That reading turns a graph into a number a specification can use: the shelf meets its limit for loads up to about sixty-six newtons.

Last, a graph from a product's own data sheet. The bike light's sheet plots its battery charge on full beam against time in hours. The curve starts at a hundred per cent and falls as the hours pass, a little faster towards the end. The low-battery warning comes on at twenty per cent. Reading the curve, when does the warning come on at full beam? At four hours, read across from the warning level to the curve, then down. Now a rider commutes forty-five minutes each way on full beam, and the time axis is in hours. How much charge is left after the ride home? Seventy-four per cent of the charge is left. Two rides of forty-five minutes make ninety minutes, which is one point five hours. Up from one point five hours to the curve, then across: seventy-four per cent. Now, what does the curve say about the five hours on the box? On full beam the battery is nearly flat at four and a half hours, so full beam cannot last five hours. The box's figure must be for a lower setting. Written as a specification line, it becomes: on full beam, at least four hours before the low-battery warning.

To finish, four questions that take these graph habits somewhere new. A test sets the temperature and times how long glue takes to set. Which goes across? The temperature, because it is the one that was set. The setting time is measured, so it goes up. Next: data up to thirty-six, ten big squares up the side. What step goes up? Fives, up to fifty. Steps of two would stop at twenty, and an odd step like four is hard to read. Back on the shelf graph now: up to what load does it sag four millimetres or less? About fifty-three newtons. Across from four millimetres to the line, then down. Here's the last: a value read off a graph always carries what? Its unit, such as fifty-three newtons or seventy-four per cent. And the bike light: up to five hours is true on a lower setting, and on full beam the data sheet's curve shows four hours to the warning.

This one closes the chapter on number, units and data, and every video in it works alone, so your thumbs up shows which ones are done. If you nailed graphs, put a thumb on this one and it is off your list. If the reading still wobbles, keep it saved, since it settles after a night's sleep.

That completes Maths skills: number, units and data. The next chapter is Maths skills: angles, area, volume and material costs.

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