COMM5000 Chap.1 Describing Data for Business
Describing Data for Business
Learn to classify variables, choose charts and numerical summaries, describe distribution shape, and interpret covariance and correlation without overstating what association can establish. Begin by naming the observational unit and target population. A column has meaning only in relation to the entity recorded in each row, its unit and the process that created it.
Categorical variables support frequency or proportion comparisons, while numerical variables support distributions, centres and spreads. Bar charts compare categories; histograms reveal the shape of one numerical variable; scatterplots show how two numerical variables vary together. Check missing values, duplicates and impossible entries before a polished display makes them harder to notice.
For a roughly symmetric distribution, the mean and standard deviation can provide an effective summary. For a skewed distribution, the median and interquartile range often represent the middle more robustly, but unusual observations may remain operationally important. Report them rather than deleting them by convenience. Covariance describes joint movement in original units, while correlation standardises linear association.
Neither coefficient replaces the scatterplot or establishes a causal mechanism. A complete business insight states the pattern, the population and period represented, the statistic and unit, and the main limitation. If groups or time periods have different distributions, show them separately before compressing everything into one overall number. Every descriptive choice should be traceable to the question it answers.
What this chapter covers
- 01
Observational units and variable types
- 02
Graphical summaries
- 03
Centre and spread
- 04
Covariance and correlation
- 05
Business interpretation
Worked example · free
Mean versus median under skew
- +1The four marks used here are not an official university marking scheme. Compute mean 25/5 = 5 days.
- +1Identify median 3 days.
- +1Calculate sample standard deviation sqrt(82/4) = 4.53 days.
- +1Use the median for a typical delivery while separately flagging the 13-day delay.
Key terms
- Observational unit
- The entity represented by one row of a dataset.
- Interquartile range
- The spread of the middle half of ordered observations.
- Correlation
- A standardised measure of the direction and strength of linear association.
Describing Data for Business FAQ
When should I use the median?
Use the median when skew or extreme observations make the mean unrepresentative of the middle case. Report the unusual observations separately when they remain important to the business decision.
Does correlation show causation?
No. Correlation compresses linear association and can reflect confounding, selection, reverse direction or other structures. A causal statement needs an appropriate design and supporting assumptions.
How do I turn a summary into a business insight?
State the observational unit, population and period first. Describe the visible pattern with its unit, then choose centre and spread that fit the shape. Identify unusual observations without deleting them by convenience. If comparing variables, report association rather than mechanism and show the scatterplot before compressing the relationship into correlation.
Finish with a bounded implication for the decision and one next check that could change it, such as validating an extreme value, separating segments or collecting a missing group. This structure keeps a descriptive result useful while preventing the interpretation from becoming stronger than the data.
Assessment move
For each dataset, write the observational unit, target population and variable types before opening a chart menu. Build a small audit table with one row for the proposed display, one for the numerical summary and one for the decision sentence. For every chart, label axes and units, check whether the scale could exaggerate a small difference, and identify any values hidden by aggregation.
For every numerical variable, describe shape, centre, spread and unusual observations together. Recalculate the mean, median, range and sample standard deviation on a five-value example until the denominator and interpretation are automatic. Then explain why the preferred centre fits the shape. For bivariate data, draw the scatterplot first and note direction, form, strength and outliers before calculating correlation.
Practise rewriting causal-sounding statements as accurate association statements. Finish by asking which subgroup, time period or data-quality check could overturn the insight. In assessment writing, place the numerical result immediately beside its business meaning so a reviewer can verify that the sentence matches the evidence.
Use the final pass to confirm every number retains its unit and every claim names the represented population rather than implying a universal pattern. Add a second pass devoted to aggregation. Compare the overall distribution with relevant segments and look for a reversal or a mixture that the combined statistic conceals.
For a categorical result, compare both counts and proportions because unequal group sizes can change the story. For a numerical result, ask whether one segment creates the skew or extreme values. Rebuild one chart with an alternative but defensible scale and check whether the interpretation changes. If it does, explain which design choice drives the difference.
Keep a data-quality log that records missingness, duplicate handling and any exclusion rule before the outcome is summarised. When writing the final insight, separate what the data display directly from the business explanation proposed for it. The first is evidence; the second is a hypothesis to investigate.
Close with a specific next check, such as validating a suspect value, collecting a missing segment or examining the relationship over time.
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