OCR GCSE Mathematics (J560) — Statistics
Have you ever tried filtering an online store by both the brand and the color at the same time? A classification table (frequently called a two-way table in exams) applies this exact logic to organize data by two or more characteristics simultaneously. These tables are ideal for sorting categorical data (like hair color) or discrete data (like the number of pets).
The table forms a grid where each intersection is a cell that records the frequency of that specific sub-category. To verify your table is perfectly balanced, the sum of all row totals and the sum of all column totals must both equal the grand total located in the bottom-right cell.
A vet clinic treats 50 animals in one day. 30 of the animals are dogs and the rest are cats. 18 of the dogs are given vaccines. A total of 25 animals are given vaccines. Construct a two-way table to display this information and find out how many cats did not receive a vaccine.
Step 1: Design the grid with categories and totals.
Step 2: Insert the known values and calculate the missing values by ensuring rows and columns sum to their totals.
| Vaccine | No Vaccine | Total | |
|---|---|---|---|
| Dogs | 18 | 12 | 30 |
| Cats | 7 | 13 | 20 |
| Total | 25 | 25 |
| 50 |
Calculations:
When analysing results, a single bar isn't always enough to show how different sub-groups performed. For grouped data, a multiple bar chart places bars for different sub-groups side-by-side. Alternatively, a composite bar chart stacks the sub-categories vertically into a single bar. In both types, the bars must maintain equal widths and equal gaps, and a legend is mandatory to identify the different segments.
To identify patterns in these charts, you must use the legend to compare specific data sets:
In a standard stacked bar, the overall height indicates the total frequency. To calculate the value of a specific higher section, you must subtract the lower boundary on the y-axis from the upper boundary. In a percentage composite bar chart, all bars reach exactly 100%. To find an absolute frequency from a percentage graph, use:
A percentage composite bar chart shows transport for 160 students. The 'Bus' segment starts at 35% and ends at 80%. Calculate the number of students who travel by bus.
Step 1: Calculate the percentage of the segment: . Step 2: Substitute into the formula: . Step 3: Final value: students.
A time series graph plots numerical values against time (e.g., quarters) using straight line segments. To analyse these graphs effectively, you must distinguish between the long-term direction and short-term patterns.
Example: Umbrella Sales (2021–2023)
Because fluctuations can hide the trend, statisticians use smoothing. This is done by calculating an n-point moving average, which averages successive values to reveal the underlying pattern.
Calculate the first two 3-point moving averages for: Mon = 15, Tue = 21, Wed = 18, Thu = 27.
Step 1: First average (Mon-Wed): . (Plot at Tuesday). Step 2: Second average (Tue-Thu): . (Plot at Wednesday).
Students often forget to include a 'Total' row and a 'Total' column when asked to design a two-way table, which loses 'Design' marks.
For 'Analyse' or 'Compare' questions on bar charts, you MUST support your observations with figures read from the chart (e.g., 'Category A is 10 units higher than Category B').
When calculating values from higher sections of a composite bar chart, remember to subtract the bottom y-axis value from the top y-axis value.
For 2-mark 'describe the pattern' questions on time series, state one point about the overall trend and one point about the seasonal variation to secure both marks.
When predicting future values from a time series, always state your assumption that the current trend and seasonal patterns will continue.
Classification table
A systematic grid used to sort categorical or discrete numerical data by two or more characteristics simultaneously.
Two-way table
A specific type of classification table used to compare two different categorical variables against each other.
Categorical data
Data that can be sorted into distinct groups or named categories (e.g., color, type of animal).
Discrete data
Numerical data that can only take certain values, usually whole numbers (e.g., number of people).
Frequency
The number of times a particular value or category occurs in a data set.
Cell
The intersection of a row and a column in a table representing a specific sub-category.
Grand total
The overall sum of all data points in a two-way table, found in the bottom-right corner.
Multiple bar chart
A chart that places bars for different sub-groups side-by-side within each main category to allow for easy comparison.
Composite bar chart
A chart where sub-groups are stacked on top of each other within a single bar to show both individual components and total frequency.
Legend
A key using colors or patterns to identify what each bar or segment represents in a chart.
Mode
The category or value that occurs most frequently in a data set. In bar charts, it is identified as the tallest bar or the largest individual segment within a stack.
Percentage composite bar chart
A stacked bar chart where every bar represents 100%, showing the relative proportion of subcategories.
Absolute frequency
The actual number of occurrences (frequency) as opposed to a percentage or relative value.
Time series
A sequence of data values recorded at successive, equally spaced points in time.
Trend
The general long-term direction of movement in a data set (e.g., upward or downward).
Seasonal variation
Regular, predictable, and repeating patterns that occur within a fixed time period on a time series graph.
Fluctuations
Short-term, unpredictable upward and downward movements in a data set.
Smoothing
The process of removing fluctuations from time series data (often using moving averages) to make the trend clearer.
n-point moving average
The arithmetic mean of a fixed number of consecutive data points in a time series.
Put your knowledge into practice — try past paper questions for Mathematics
Classification table
A systematic grid used to sort categorical or discrete numerical data by two or more characteristics simultaneously.
Two-way table
A specific type of classification table used to compare two different categorical variables against each other.
Categorical data
Data that can be sorted into distinct groups or named categories (e.g., color, type of animal).
Discrete data
Numerical data that can only take certain values, usually whole numbers (e.g., number of people).
Frequency
The number of times a particular value or category occurs in a data set.
Cell
The intersection of a row and a column in a table representing a specific sub-category.
Grand total
The overall sum of all data points in a two-way table, found in the bottom-right corner.
Multiple bar chart
A chart that places bars for different sub-groups side-by-side within each main category to allow for easy comparison.
Composite bar chart
A chart where sub-groups are stacked on top of each other within a single bar to show both individual components and total frequency.
Legend
A key using colors or patterns to identify what each bar or segment represents in a chart.
Mode
The category or value that occurs most frequently in a data set. In bar charts, it is identified as the tallest bar or the largest individual segment within a stack.
Percentage composite bar chart
A stacked bar chart where every bar represents 100%, showing the relative proportion of subcategories.
Absolute frequency
The actual number of occurrences (frequency) as opposed to a percentage or relative value.
Time series
A sequence of data values recorded at successive, equally spaced points in time.
Trend
The general long-term direction of movement in a data set (e.g., upward or downward).
Seasonal variation
Regular, predictable, and repeating patterns that occur within a fixed time period on a time series graph.
Fluctuations
Short-term, unpredictable upward and downward movements in a data set.
Smoothing
The process of removing fluctuations from time series data (often using moving averages) to make the trend clearer.
n-point moving average
The arithmetic mean of a fixed number of consecutive data points in a time series.
