FIT4005 Chap.8 Descriptive Statistics and Data Visualisation
Descriptive Statistics and Data Visualisation
Descriptive statistics summarise what a dataset contains so you can see its key characteristics before drawing any conclusions. Week 8 is conceptual and practical rather than mathematical. It defines datasets in terms of observations, variables and data points, distinguishes primary, secondary and open data, and separates descriptive from inferential statistics.
You practise measures of centre and spread on a small worked dataset, see how one outlier moves the mean and range but not the median and interquartile range, and learn to read skew from the gap between mean and median.
The chapter ends with data storytelling: choosing a chart by the relationship you want to show and building a narrative for a specific audience.
The week's studio uses a real public-opinion data set on concerns about artificial intelligence across many countries.
Students compute centre and spread for each concern, compare means with medians to judge skew, look for outliers and their effect on range and interquartile range, choose two chart types for a subset of countries, and then pitch a short data story to an audience they choose. The same workflow applies to any dataset you meet in practice.
What this chapter covers
- 01
Quantitative data in industry
- 02
Observations, variables and data points
- 03
Primary, secondary and open data
- 04
Descriptive and inferential branches
- 05
Mean, median and mode
- 06
Range, interquartile range and standard deviation
- 07
Outliers and skew
- 08
Choosing charts and telling a data story
Worked example · free
Summarise a skewed dataset
- +1Sum the values: 4 + 5 + 5 + 6 + 7 + 8 + 28 = 63, so the mean is 63 divided by 7, which is 9.
- +1Sort the values; the fourth of seven is the median, 6.
- +1Range is 28 minus 4, which is 24.
- +1The mean exceeds the median because the week with 28 crashes pulls it up, so the median of 6 better describes a typical week; report the 28 separately.
Key terms
- Observation
- One row of a dataset, also called a record, tuple or trial.
- Variable
- One column of a dataset, also called a feature, field, attribute or predictor.
- Secondary data
- Existing data collected by someone else, which saves time but may not suit the problem at hand.
- Open data
- Data anyone is free to use, reuse and redistribute, subject at most to preserving provenance and openness.
- Interquartile range
- The spread of the middle half of the data, from the first to the third quartile.
- Outlier
- A value far from the rest of the data that can distort the mean and the range.
Descriptive Statistics and Data Visualisation FAQ
Does Week 8 require mathematical derivations?
No. The lecture describes its approach as conceptual and practical, focused on applying measures rather than deriving them. You should be able to compute and interpret the measures and choose a suitable chart.
How do I know whether a distribution is skewed?
The studio asks you to compare the mean and the median. When they are close the data are roughly symmetric; when the mean is well above the median, a few high values are pulling it, which suggests right skew.
Which chart should I use for survey sentiment?
The Financial Times Visual Vocabulary used in the week suggests a diverging stacked bar for sentiment, a histogram or box plot for distributions, a scatterplot for correlation, and an ordered bar chart for rankings.
What questions should I ask of any dataset?
Ask who collected it, how it was collected, whether it is representative or affected by sampling bias, and whether there are many outliers. The lecture notes these are hardest to ask about data close to you.
Which software tools does the unit mention for statistics?
The lecture compares SPSS, which is user-friendly but limited with large data, R, which is free with a steep learning curve, Stata, which is costly with limited graphics, MATLAB, which is not built for statistics, and Excel for basic means and standard deviations.
Assessment move
Practise on small invented datasets until computing the mean, median, range and interquartile range takes a minute, then spend your effort on interpretation: what the gap between mean and median says, what the outlier is, and which summary you would report. For charts, decide the relationship first and the chart second, and annotate every axis.
Rehearse a two-minute data story for a non-specialist audience, because communication to different audiences is one of the learning outcomes listed for Assignment 2. Finish every summary with one sentence that tells a non-specialist what the numbers mean for the decision at hand.
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