Running the analysis, and chapter reference
JASP, PocketStat, descriptive statistics in JASP, reporting statistics, statistics glossary, formula review
Parts 1 to 3 built every summary by hand, five values at a time. The software does the same arithmetic on all 200 at once.
That removes the arithmetic and leaves the two judgements that were always yours: which summary the variable supports, and what the result means for the branch. This page runs the chapter’s analysis both ways, in JASP and in PocketStat, then turns the output into the paragraph a manager will read.
The key terms and the formula review at the foot cover all four parts, with every term linked back to the section that defines it.
Running the analysis
Each route reaches the same answer. Use whichever suits the machine you have, and name it in your write-up.
In JASP
- Open JASP and choose Open, then Computer, and select
DMM_Teaching_Data_Full.csv. - Check the measurement icon beside every variable you intend to use. CSV import marks almost everything as scale, and a nominal variable read as scale will let you calculate a meaningless mean.
- Choose Descriptives, then Descriptive Statistics.
- Move your variables into the Variables box.
- Under Statistics, tick mean, median, standard deviation, minimum, maximum and quartiles.
- Under Plots, tick the distribution plot and the boxplot.
The tutorial takes this apart step by step, with a screenshot at each click.
In PocketStat
PocketStat runs inside this page. Nothing installs, nothing uploads, and your data stays on your own machine.
- Load
DMM_Teaching_Data_Full.csvfrom the Data tab, or pick the built-in demo dataset. - Check the type shown beside each variable, as you would in JASP.
- Choose Descriptive statistics from the technique list.
- Select your variables and read the summary table and the plot together.
For the distribution shape and the histogram, choose Distribution shape instead.
Reporting the result
A descriptive result is finished when it becomes a sentence a manager can act on.
For a categorical variable. State the total, the largest category with its share, and what follows.
Of 200 respondents, 124, or 62 per cent, held standard tickets. That is the largest group by some distance, so any pricing change reaches most of the customer base through that one category.
For a numerical variable. State the centre, the spread, and the decision-relevant tail.
Half of customers waited 46 minutes or less, and the middle half waited between 38 and 53 minutes. Nineteen customers, just under one in ten, waited more than an hour, and two waited over 75 minutes.
For the whole question. Bring both together and name the limit.
Waiting time was recorded for 200 customers at one branch over one month. Half waited 46 minutes or less and the middle half fell between 38 and 53 minutes, so the service is consistent for most customers. The exception is the 19 customers who waited over an hour, two of them over 75 minutes, and those are where any service-standard breach and most complaints will concentrate. These figures describe this branch in this month and say nothing about other branches.
Weak reporting states the procedure: “descriptive statistics were calculated”. Strong reporting states the finding, its size, and its consequence.
Chapter review
Describe before you decide. Settle the variable type first, because it governs every summary and every graph that follows. Report centre and spread together, because either alone misleads. Prefer the cumulative view when the question is about a standard or a threshold. Mark the point where you move from describing your data to claiming something about a wider population.
Key terms
Every term links to the section that defines it, and the three groups follow the three parts of the chapter, so this doubles as a revision map.
Part 1, foundations
- Case
- the unit the data describe
- Variable
- a characteristic measured on each case
- Observation
- all values recorded for one case
- Datum
- a single value
- Constant
- a feature every case shares
- Population
- every case of interest
- Sample
- the subset measured
- Parameter
- a number describing a population
- Statistic
- a number describing a sample
- Sampling error
- the gap left by measuring a sample
- Non-sampling error
- every other source of error
- Descriptive statistics
- summarising the data held
- Inferential statistics
- reasoning from a sample to a population
- Proportion
- a count divided by the total
Part 2, variables and displays
- Nominal
- named categories
- Ordinal
- ordered categories with unequal gaps
- Interval
- equal gaps, no true zero
- Ratio
- equal gaps and a true zero
- Discrete
- counted
- Continuous
- measured
- Independent variable
- the proposed explanation
- Dependent variable
- the outcome
- Frequency
- how many in a category
- Relative frequency
- the proportion in a category
- Cumulative frequency
- how many up to a point
Part 3, centre and spread
- Mean
- the arithmetic average
- Median
- the middle value
- Mode
- the most frequent value
- Bimodal
- having two modes
- Range
- maximum minus minimum
- Deviation
- a value minus the mean
- Variance
- the mean squared deviation
- Standard deviation
- the square root of the variance
- Coefficient of variation
- the standard deviation as a share of the mean
- Percentile
- a position in the ordered data
- Quartile
- a quarter boundary
- Interquartile range
- the third quartile minus the first
- Fence
- the 1.5 IQR boundary
- Skew
- asymmetry
- Outlier
- a value beyond a fence
Formula review
| Quantity | Formula |
|---|---|
| Sample mean | \(\bar{x} = \dfrac{\sum x}{n}\) |
| Median position | \(\dfrac{n+1}{2}\) in the ordered data |
| Mode | The value with the highest frequency. Read off a frequency table, never calculated |
| Range | maximum \(-\) minimum |
| Deviation | \(x - \bar{x}\) |
| Sample variance | \(s^2 = \dfrac{\sum (x - \bar{x})^2}{n-1}\) |
| Sample standard deviation | \(s = \sqrt{s^2}\) |
| Coefficient of variation | \(CV = \dfrac{s}{\bar{x}} \times 100\%\) |
| Interquartile range | \(IQR = Q_3 - Q_1\) |
| Outlier fences | \(Q_1 - 1.5 \times IQR\) and \(Q_3 + 1.5 \times IQR\) |
| Relative frequency | \(\dfrac{f}{n}\) |
| Percentage | relative frequency \(\times \, 100\) |
References and further reading
- OpenStax. (2023). Introductory Business Statistics 2e. Rice University.
- Pallant, J. (2016). SPSS Survival Manual (6th ed.). Open University Press.
- Villa College. (2026). BUSS2111 Decision Making for Management Module Handbook 2026/27.