Pictorial and Graphical Representation of Data

Which diagram, and why?

This part of the course looks like a list of chart names to memorise. It is not. Almost every question comes down to one thing: does this representation suit this data, and what does it show? So learn each diagram with the data type it belongs to. A representation that is right for categories is wrong for continuous measurements, and an examiner will always know which you were given.

Two big families

Most of the diagrams in this section fall into one of two jobs. Getting the job right narrows the choice immediately.

Match each task to the representation that suits it

Continuous and grouped

You have the heights of 200 people, grouped into classes of equal width. Which representation is designed for exactly this?

• A histogram, with the bars touching
• A bar chart, with gaps between the bars
• A pie chart
• A pictogram

What is Higher only, and the rule that matters

Some of this sub-section is Higher tier only, so check which paper you are sitting: • Comparative pie charts, and comparative 2D and 3D representations • Frequency density, and histograms with UNEQUAL class widths • Skewness by CALCULATION, where the formula is given The rule worth more than the list: once the class widths are unequal, the height of each bar is no longer the frequency. It is the frequency density, which is frequency divided by class width, and the FREQUENCY IS THE AREA of the bar. Reading a height as a frequency on an unequal-width histogram loses the whole question.

Histograms

Select the TWO correct statements about histograms.

• The bars touch, because the horizontal scale is continuous
• When class widths are unequal, the frequency is represented by the AREA of each bar
• The height of a bar always gives the frequency, whatever the class widths
• A histogram is the right choice for separate named categories

The specialist four

These come up precisely because they are distinctive. Each exists to do one job well:

Match each specialist diagram to what it is for

Find the tail

Skew is named for the side the TAIL runs to, not for where the peak sits. Tap the tail of this distribution.

Which way is it skewed?

That distribution peaks near the left and trails away to the right. What is it called?

• Positively skewed, because the tail runs to the right
• Negatively skewed, because the peak is on the left
• Symmetrical, since it has one clear peak
• It has no skew, because skew only applies to histograms

Draw the pie chart

Put the steps of drawing a pie chart from a frequency table into order.

• Add the frequencies to find the total
• Divide 360 by that total to find the degrees per item
• Multiply each category frequency by that figure to get its angle
• Check the angles sum to 360 degrees before drawing anything
• Draw and label each sector, or add a key

Bar chart or histogram

Separate categories get a bar chart, with _____ between the bars; grouped continuous data gets a _____, with the bars touching. When class widths are unequal the bar height is the _____ and the frequency is the _____ of the bar. A distribution whose tail runs to the right is _____ skewed.

Choose and justify

A researcher has recorded the exact journey time to school, in minutes, for 300 students, and wants to show the shape of the distribution and compare boys with girls. Recommend how to represent the data, and justify your choice.

• Name the representation you would use to show the shape of the distribution, and say why it suits this data type
• Name a representation that would let the two groups be compared directly, and say how it does that
• Explain what you would have to be careful about if the class widths were not all equal
• Give one thing your chosen representation does NOT show, so the recommendation is honest
• Use the words continuous, distribution and skew correctly at least once each