Independent study
independent study, descriptive statistics exercises, variable audit, self-check, business statistics practice
Self-learning Descriptive foundations
Acquisition
1 Read and make notes
⏱ 60 min
Read the assigned sections of this chapter and turn them into a short study sheet.
Production
2 Guided practice
⏱ 75 min
Complete guided practice on variables, scales, frequency distributions and the main descriptive statistics.
Production
3 Independent analysis
⏱ 75 min
Repeat the tutorial analysis in your own time and save a clean copy of your output.
Production
4 Reflection or study note
⏱ 60 min
Write a short study note on when a mean, median, or frequency table is most useful for management reporting.
Assessment
5 Checkpoint
⏱ 90 min
Complete the chapter checkpoint quiz and upload your variable-audit note.
This page is for your own study and your preparation for the final examination. It is ungraded, and everything you do here stays with you. The chapter’s graded work is the checkpoint quiz.
You may use Google NotebookLM on this page: to quiz yourself on the exercises, to explain a step a second way, or to turn your notes into a revision sheet. Keep what you produce for your exam revision. NotebookLM can make mistakes, so check each answer against the chapter before you rely on it.
Reading
The assigned reading is this chapter. It runs to about 12,200 words in total. This hour covers the explanatory sections, roughly 7,600 words, which take close to an hour to read closely, pen in hand.
The 12 worked examples and the 10 Try It exercises belong to activity 2, guided practice, which has 75 minutes of its own. Read the explanation in this hour and work the exercises in the next.
| Read | Minutes |
|---|---|
| Part 1, foundations | 18 |
| Part 2, variables and displays | 18 |
| Part 3, centre and spread | 18 |
| Running the analysis and reference | 6 |
Your study sheet should fit on one side. A longer sheet usually means you copied material instead of selecting it. The chapter’s Key terms and Formula review sections are a good check on it: if your sheet covers those, you have the chapter.
If a section went too fast. OpenStax, Introductory Business Statistics 2e, is free to read at openstax.org. Chapter 1 covers sampling and data, and chapter 2 covers descriptive statistics. Both cover the same topics at a slower pace with a second set of examples. This is optional and sits outside the hour.
Try It exercises
Work these before checking the solutions.
Try It A: Identify cases and variables
A logistics firm records, for every delivery last month: delivery ID, depot, driver, distance in kilometres, minutes taken, and whether the delivery was on time.
State the case, list the variables, classify each variable’s measurement scale, and say which variable would be dependent if the question were “what makes deliveries late?”
Try It B: Match the summary to the variable
For each variable, name the single most appropriate measure of centre and justify it in one sentence.
| Variable | Most appropriate centre | Why |
|---|---|---|
| Payment method, one of four options | ||
| Customer rating, 1 to 5 | ||
| Delivery time in minutes, right-skewed | ||
| Number of items per order |
Try It C: Mean and median
Nine monthly order values, in thousands: 12, 14, 15, 15, 18, 19, 22, 26, 140.
Calculate the mean and the median. State which better describes a typical month, and what the gap between them tells you about the shape.
Try It D: Graph choice
For each question, name the graph and give one reason.
- Has the complaint rate changed across the last eight quarters?
- Do customers who wait longer report lower satisfaction?
- How is order value distributed?
- What share of orders comes from each of three channels?
- Does delivery time differ between four depots?
Self-check
Use this list to check your own work before the checkpoint quiz.
| Check | |
|---|---|
| ☐ | Every variable in my audit has a scale, and I can defend the two arguable ones |
| ☐ | My frequency table includes relative frequency in addition to counts |
| ☐ | My grouped table has no gaps and no overlaps at the interval boundaries |
| ☐ | My grouped table includes a cumulative column |
| ☐ | I report centre and spread for every numerical variable |
| ☐ | My graph type matches the variable type |
| ☐ | The vertical axis in my bar chart output starts at zero |
| ☐ | My paragraph states the limitations of the evidence |
| ☐ | I have said whether I used JASP or PocketStat |
| ☐ | My paragraph is under 120 words |
Review questions
- Why does a sample statistic carry uncertainty when a population parameter does not?
- Give an example of a question that description alone can answer.
- Why does the sample variance divide by n minus 1?
- A mean of 480 sits with a median of 395. What shape is the distribution, and which figure would you report as typical?
- When is the mode the only defensible measure of centre?
- Why is a truncated axis more misleading on a bar chart than on a line chart?
Solutions
Solutions to Try It 1.1 to 1.10 sit directly beneath each task in the chapter, so you can check an answer without losing your place. The four tasks below are answered here.
The case is the delivery. The variables are delivery ID, depot, driver, distance, minutes taken, and on-time status.
Scales: delivery ID is nominal, an identifier with no inherent measurement. Depot and driver are nominal. Distance and minutes are ratio and continuous. On-time status is nominal.
If the question is “what makes deliveries late?”, then minutes taken or on-time status is the dependent variable. Depot, driver, and distance are the candidate independent variables.
| Variable | Centre | Why |
|---|---|---|
| Payment method | Mode | Nominal, so no other measure is defined |
| Customer rating 1 to 5 | Median | Ordinal: the categories are ordered, but the gaps are not guaranteed to be equal |
| Delivery time, right-skewed | Median | The tail of slow deliveries would pull the mean above the typical value |
| Number of items per order | Mean | Ratio and usually roughly symmetric, so the mean uses all the data |
The total is 281, so the mean is 31.2 thousand. When ordered, the middle value of the nine observations is 18 thousand.
The median describes a typical month. The mean sits above eight of the nine values because of the single 140, which is either an exceptional month or an error to verify.
The difference between them, with the mean far above the median, indicates right skew.
- Line chart. The data involves ordered time, and the question concerns change.
- Scatterplot. The analysis involves two continuous variables and a question about their relationship.
- Histogram. The analysis involves one continuous variable and a question about its distribution.
- Pie chart, for three categories, or a bar chart. Both work. A pie chart shows the share of a whole. A bar chart compares the counts.
- Boxplot, one per depot. Four distributions are compared at once, with the spread visible.
Key takeaways
- Settle the variable type before choosing any summary or any graph.
- Report centre and spread together. Reporting one without the other hides the spread.
- Cumulative frequency answers threshold questions directly.
- The difference between mean and median reveals skew without a graph.
- Say when you have stopped describing the sample data and started claiming something about a wider population.