One-page revision sheet

• The mode is the value that occurs most often.
• The median is the middle value — but only once the data is in order.
• With an even number of values, the median is halfway between the middle two.
• The range is largest − smallest. It measures spread, not average.
• With n values in order, the median is in position (n + 1) ÷ 2.
• The mode must be one of the values; the median need not be.
• A set can have no mode, and saying so is a proper answer.
• The mode is the only average that works for words — a modal colour makes sense, a mean colour does not.
• The range sees only the two ends, so two very different sets can share one.

Key words: mode  ·  median  ·  range  ·  average  ·  spread  ·  data set

• Mean = total ÷ how many.
• It shares the total out equally: what everyone would have if they all had the same.
• Rearranged: total = mean × how many. That step unlocks most mean problems.
• The mean need not be one of the values — 1.6 pets is a perfectly good mean.
• It must lie between the smallest and the largest value.
• From a frequency table: multiply each value by its frequency, add those, then divide by the total frequency.
• To find a missing value: work out the total the mean demands, then subtract what you already have.
• The mean uses every value, so one extreme reading moves it a long way.
• That sensitivity is its weakness, and the subject of the next section.

Key words: mean  ·  total  ·  frequency  ·  average  ·  per

• All three of mode, median and mean are averages. They choose the representative value differently.
• Mode: use it for categories and for “which is most popular”. It is the only one that works for words.
• Median: use it when there is an outlier or the data is lopsided — house prices, salaries.
• Mean: use it when the values are close together with no extremes. It uses every value.
• An outlier moves the mean a long way and the median hardly at all.
• Do not silently delete an outlier. Investigate it, and say what you decided.
• Always quote a range alongside an average — the average alone says nothing about spread.
• A smaller range means more consistent.
• In an examination the reason earns the mark, not the name of the average.

Key words: outlier  ·  appropriate  ·  distort  ·  typical  ·  consistent  ·  categorical data

• A bar chart compares separate categories. Read the height against the scale.
• A line graph shows how something changes over time. The joined points show the trend.
• A pie chart shows shares of a whole. The sectors must total 360°.
• In a pie chart of N people, one person is worth 360 ÷ N degrees.
• To go the other way: people = angle ÷ (360 ÷ N).
• A percentage becomes an angle by taking that percentage of 360°.
• A bar chart's scale should start at zero. If it does not, the differences look bigger than they are.
• A pie chart alone does not tell you how many people were asked — the total must be stated.
• Always read the numbers from the scale, never judge by the picture alone.

Key words: bar chart  ·  line graph  ·  pie chart  ·  sector  ·  scale  ·  trend

• To compare two data sets, quote an average and a range. Either one alone is half a comparison.
• The average says what is typical; the range says how much it varies.
• A smaller range means more consistent.
• Write the comparison as a sentence about the situation, with the numbers in it.
• A trend is the general direction. One dip does not end a rising trend.
• A trend describes what has happened; it does not promise what comes next.
• A small sample gives an unreliable conclusion — Unit 6's idea, used here.
• A biased sample is worse than a small one: no amount of correct arithmetic can fix it.
• Mention the sources of variation: the weather, the time of day, who was asked, how it was measured.

Key words: compare  ·  consistent  ·  trend  ·  sample  ·  bias  ·  variation