Charts: frequency tables, bar charts, pie charts and histograms

Two charts are drawn from the same survey of two hundred students choosing a fastening for a school bag. One shows the zip as the clear winner. The other makes the magnetic clasp look just as popular. Same numbers, same survey. One of those charts is misleading, and you can spot which without reading a single number.

Charts here lean on percentages. If those feel shaky, the video on fractions and percentages covers them, and otherwise this one stands alone.

Start with a frequency table. Frequency means how many times something turns up, so the table lists each answer with how many times it was given. Sixty students were asked which material they would choose for a phone case. Silicone got twenty-two votes, TPU fourteen, polycarbonate twelve, leather six and wood veneer six. TPU is thermoplastic polyurethane, a flexible plastic. Each material goes in a row with its frequency, and the last row is a total. Twenty-two plus fourteen plus twelve plus six plus six is sixty, the number of students asked. If that total had come to fifty-eight, what would it tell you? That two answers were missed or miscounted. The total is the check on the tally. Next, the bar chart. A bar chart is for separate categories, things like materials that have no order of size. To draw one, give each material one bar, every bar the same width, with equal gaps between them. Across the bottom goes the axis title, phone case material. Up the side goes number of students, on an even scale that starts at zero. The biggest value is twenty-two, so count up in fives to twenty-five. Before plotting, say what one small square is worth. If each small square is one student, the silicone bar stops on twenty-two, not near it. And if the axis says percentage, change the counts into percentages before you plot. Then the finish, a step of its own: both axis titles, and a title for the whole chart, such as phone case material chosen by sixty students. Now back to the fastening charts. What three things are wrong with the misleading one? The misleading one has axes with no labels, a scale that does not start at zero, and bars of different widths. The clasp's bar is drawn fatter, so it looks as big as the zip's, and with no labels and no zero there is nothing to check it against. Bar charts are usually drawn well. One examiner's report records: The vast majority of candidates demonstrated that they knew what bar graphs were and how to draw them accurately. On a question where a bar chart had to be drawn, another report says: Where candidates lost marks it was for not labelling the axis correctly or for drawing the bars to different thicknesses. Some candidates drew line charts instead of a bar chart. The habit that fixes all three is the same finish every time: equal bars, labelled axes and a title, drawn as bars and never joined into a line. Now the designer says most students want silicone. Is that right, and why? No. Silicone is the most popular, but twenty-two out of sixty is about thirty-seven per cent, which is not most students. A fair decision is silicone first, with TPU as the next option to test.

Pie charts come next. A pie chart splits a full circle by share, and a full circle is three hundred and sixty degrees. The whole circle stands for a hundred per cent. So one per cent is three hundred and sixty divided by a hundred, which is three point six degrees. Every angle is its percentage times three point six. If you are given counts instead, the angle is the count over the total, times three hundred and sixty. Back to the two hundred students and their fastenings. Zip got forty-five per cent, magnetic clasp twenty-seven point five, hook-and-loop seventeen point five, and buckle ten. Hook-and-loop is the rip-apart fastening on trainers. Zip first: forty-five times three point six is a hundred and sixty-two degrees. What angle does the magnetic clasp get in the pie chart? The magnetic clasp gets ninety-nine degrees. Twenty-seven point five times three point six is ninety-nine. Hook-and-loop is seventeen point five times three point six, sixty-three degrees. Buckle is ten times three point six, thirty-six degrees. Check: a hundred and sixty-two plus ninety-nine plus sixty-three plus thirty-six is three hundred and sixty. To draw it, rule one radius, a line from the centre to the edge. Put the protractor's centre on the circle's centre, measure a hundred and sixty-two degrees, and draw the next line. Measure each sector, each slice, from the last line you drew. Then the finish: label every sector, or add a key, and give the chart a title. On a question where a pie chart had to be completed, one examiner's report says: Where no working was shown, and the graphic response was inaccurately drawn marks were lost. Students need to be reminded to show working to gain method marks where correct understanding has been shown. The commentary on one marked answer to that question adds: This response correctly identifies the hybrid and diesel cars but has not added the pattern key which is required for maximum credit. So the fix comes in two parts. Write the three point six line and every angle before you draw, and finish with the key, so the method shows even if a line is a degree out.

Last, histograms. A histogram is for measurements sorted into groups, such as hand spans in millimetres, not for separate categories. A designer measures the hand spans of forty Year Ten students to size a games controller. The first group is a hundred and sixty to under a hundred and seventy millimetres, and each group after it is ten millimetres wide, up to two hundred and ten. The frequencies are three, eight, fourteen, ten and five. The horizontal axis is a number line, hand span in millimetres, from a hundred and sixty to two hundred and ten. The groups are equal, ten millimetres each, so the bars are equal widths. Should the histogram's bars touch, or have gaps between them, and why? They touch. A measurement runs on without a break, so one group ends exactly where the next one begins. Set the phone case bar chart beside this histogram and the difference is plain. Separate categories get gaps between the bars. A measured number line gets none. Up the side goes number of students, from nought to fifteen. The bar heights are three, eight, fourteen, ten and five, which total forty, so the chart checks. Then a title. Which group should the controller's grip be designed around? A hundred and eighty to under a hundred and ninety millimetres. It has the tallest bar, so it is the modal class, the group with the highest frequency. The grip is sized around that span. The eleven students below a hundred and eighty, and the fifteen at a hundred and ninety and above, are the ends to test it with.

Four quick ones now, on charts and data this video has not drawn. A sector stands for forty per cent. What angle should it be? A hundred and forty-four degrees. Forty times three point six. Next: the masses of thirty apples in grams. Bar chart or histogram, and why? A histogram, because mass is a measurement, grouped on a number line with touching bars. Now nine of thirty students chose blue. What angle is blue's sector? A hundred and eight degrees. Nine over thirty, times three hundred and sixty. A different one: besides the bars, what three things finish a chart? Labels or a key, a title on each axis, and a title for the chart. And the two fastening charts: the honest one has labelled axes, a scale from zero and equal bars, and on it the zip wins clearly.

You can dip into these videos in whatever order you need them, so the thumbs up is the tick that tells you a skill is covered. When you feel comfortable with charts, give this one the thumb and you need not come back. If drawing them still feels shaky, save it for the week ahead, because it often lands on a second viewing.

Following this one in the chapter: Plotting and reading graphs.

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