Revision notes

Every Statistics topic condensed to one page: the facts to know, the mistakes to avoid, and the formulae. Use it as a last-minute check, or print it.

Formulae for this unit

Mean $\dfrac{\text{sum of the values}}{\text{how many values}}$
Mean from a frequency table $\dfrac{\sum fx}{\sum f}$

Collecting Data & Sampling Methods

Primary data you collect yourself; secondary data comes from somewhere else.
Discrete data can be counted; continuous data is measured and can take any value in a range.
A sample should be random and large enough to represent the whole population.
A good questionnaire has clear, non-leading questions with non-overlapping answer boxes.

Watch out: Confusing discrete and continuous data, for example treating a measurement like height or time as discrete instead of continuous.

Mean, Median & Mode

Mean is the total of the values divided by how many values there are.
Median is the middle value when the data is in order; average the middle two if there is an even number.
Mode is the most common value; there can be none, one, or more than one.
The mean is affected by extreme values; the median is not.

Watch out: Forgetting to order the data before finding the median, which can give the wrong middle value.

Range & Spread

Range is the largest value minus the smallest value; it measures spread, not average.
A small range means consistent data; a large range means it is spread out.
The interquartile range is the middle 50%: upper quartile minus lower quartile.
The interquartile range ignores outliers, so it is more reliable than the range.

Watch out: Subtracting in the wrong order, giving a negative range instead of largest minus smallest.

Averages from Frequency Tables

The mode is the value with the highest frequency.
For the mean, multiply each value by its frequency, add those up, then divide by the total frequency.
Find the median position with (n plus 1) over 2, then count through the frequencies.
The total frequency is the sum of the frequency column, not the number of rows.

Watch out: Confusing the mode with the frequency itself, giving the highest frequency number instead of the data value that has that frequency.

Averages from Grouped Data

With grouped data you can only estimate the mean, because the exact values are unknown.
Use the midpoint of each class as the value, then multiply by the frequency.
The modal class is the group with the highest frequency.
The class containing the median is found from the n over 2 position.

Watch out: Giving the frequency of the modal class instead of the class interval itself as the answer.

Bar Charts & Pictograms

Bar charts have equal-width bars with gaps, and the height shows the frequency.
Leave gaps between bars for categories; a histogram for grouped data has no gaps.
A pictogram needs a key showing what one symbol represents.
Always label both axes and give the chart a title.

Watch out: Misreading the scale on a bar chart's vertical axis, especially when the gridlines increase in steps other than 1, such as steps of 3 or 4.

Pie Charts

The whole circle is 360 degrees and represents the total frequency.
The angle for a category is its frequency over the total frequency, times 360.
To read a pie chart, do the reverse: angle over 360, times the total.
Pie charts show proportions, not actual frequencies, unless the total is given.

Watch out: Comparing sector angles directly between two pie charts with different totals, without converting each angle back to an actual frequency first.

Stem and Leaf Diagrams

The stem is the first digit or digits, the leaf is the last digit, and leaves go in order.
Always include a key, such as 3 line 4 means 34.
The diagram keeps every data value, so you can still find the median and mode.
A back-to-back stem and leaf compares two data sets.

Watch out: Misreading how the stem and leaf combine to form a value, without checking the key, especially when the stem represents tens versus a different place value.

Scatter Graphs & Correlation

Scatter graphs show whether two variables are correlated.
Positive correlation means both rise together; negative means one rises as the other falls.
A line of best fit follows the trend with roughly equal points either side.
Correlation does not prove that one variable causes the other.

Watch out: Confusing positive and negative correlation, or describing a scattered graph with no clear pattern as having a correlation.

Cumulative Frequency Graphs

Cumulative frequency is a running total of the frequencies.
Plot each cumulative total against the upper boundary of its class.
The curve is an S shape; read the median at n over 2 and the quartiles at n over 4 and 3n over 4.
Reading up from a value tells you how many pieces of data are below it.

Watch out: Reading the graph in the wrong direction, such as starting from the vertical axis when a value on the horizontal axis is given, or vice versa.

Box Plots

A box plot shows five numbers: minimum, lower quartile, median, upper quartile, maximum.
The box is the interquartile range and the line inside it is the median.
Compare two box plots by their medians for average and by their spread.
A longer box or whisker on one side shows the data is skewed that way.

Watch out: Confusing the median line inside the box with one of the quartiles, especially when it is not positioned centrally within the box.

Histograms

Histograms are for grouped continuous data and have no gaps between the bars.
When class widths are unequal, the vertical axis is frequency density, not frequency.
Frequency density is frequency divided by class width.
The frequency for a class is the area of its bar, not its height.

Watch out: Confusing frequency density with frequency itself, forgetting that the height of a histogram bar is not the frequency when class widths are unequal.

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