- 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 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 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.
- 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.
- 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 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.
- 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.
- 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 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 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.
- 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 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.
