STAT1008 Chap.2 Tables and Charts for Summarising Data
Tables and Charts for Summarising Data
Tables and Charts for Summarising Data matches each display to the kind of data being summarised. One categorical variable becomes a summary table and bar chart; two categorical variables become a contingency table and side-by-side bars; one numerical variable becomes a frequency table and histogram; two numerical variables become a scatter plot.
The chapter stresses choosing the right percentage denominator, cleaning special codes before counting, picking a sensible number of class intervals, and describing a scatter plot by direction, strength and outliers. A common assessment pattern gives a small table or dataset and asks for the right summary, a chart, and two or three sentences of interpretation.
Marks depend on naming the denominator for every percentage and on describing shape, centre and spread rather than listing the numbers again.
What this chapter covers
- 01
Summary tables and bar charts
- 02
Contingency tables with row, column and total percentages
- 03
Side-by-side bar charts
- 04
Frequency tables and class width
- 05
Histograms and their shape
- 06
Scatter plots and how to describe them
Worked example · free
Build a frequency table for 60 commute times
- 1Range = 58 − 2 = 56 minutes; 56/6 = 9.33, rounded up to a width of 10 minutes.
- 1Classes (0, 10], (10, 20], …, (50, 60] contain 4, 11, 17, 14, 9 and 5 students, totalling 60.
- 1Relative frequencies are 0.067, 0.183, 0.283, 0.233, 0.150 and 0.083.
- 1Cumulative frequencies are 4, 15, 32, 46, 55 and 60.
- 1The modal class is 20 to 30 minutes and the right tail is longer than the left.
Key terms
- Contingency table
- A contingency table cross-classifies two categorical variables, with a count in each combination of their categories.
- Row percentage
- A row percentage divides a cell count by its row total, describing the column variable within one row group.
- Histogram
- A histogram is a bar plot of a frequency table for a numerical variable, with touching bars over the class intervals.
- Scatter plot
- A scatter plot graphs paired values of two numerical variables, one point per unit.
- Class midpoint
- A class midpoint is the average of the lower and upper endpoints of a class interval.
- Frequency table
- A frequency table counts how many observations of a numerical variable fall into each class interval.
Tables and Charts for Summarising Data FAQ
How do I know whether to use row or column percentages?
Ask which variable is the condition in the question. If you want to compare groups defined by the rows, divide each cell by its row total. If the groups are the columns, use column totals. Grand-total percentages describe the joint distribution of both variables.
How many bins should a histogram have?
The lecture gives a rough guide based on sample size: fewer than about five intervals for under 50 observations, five to ten for 50 to 200, and ten or more beyond 200. The aim is bins that are neither nearly empty nor so wide that shape disappears.
Why must special codes be removed before summarising?
Survey files often store answers such as refusal or don’t know as large numbers like 777 or 999. Left in a numerical column they stretch the range, distort the bins and inflate the mean, so they should be blanked or removed first.
What is the difference between a bar chart and a histogram?
A bar chart displays a categorical variable, so its bars are separated and can be reordered. A histogram displays a numerical variable over class intervals, so its bars touch and must stay in order along the measurement scale.
What should a comment on a histogram include?
Describe the shape, including skew and the number of peaks, say where the centre roughly lies, indicate the spread, and point out gaps or unusual values. Tie each remark to the units on the axis so the comment is about the data rather than the picture.
Exam move
Take any small survey you can invent and produce all four kinds of display by hand, then in Excel with a PivotTable. For every contingency table, write one sentence each using row, column and grand-total percentages so you hear how the meaning changes. For histograms, practise the range, width and round-up routine, and for scatter plots always write direction, strength, outliers and one caveat.
Practise reading each table aloud as a sentence that names its denominator, because swapping row and column percentages is the most common lost mark here. Then time yourself building a frequency table and histogram from 40 to 60 raw values, aiming for under ten minutes including the interpretation.
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