IB Business Management SLTopic 6 — The Business Management ToolkitPaper 1 & 2Core skill~13 min read
Working With Descriptive Statistics
An average tells you where the middle of the data is. It says nothing about how spread out the numbers are — and for a business, the spread is often the more useful fact. Two shops with the same average weekly sales can be completely different businesses to run.
📚 What you need to know
The mean is the total divided by how many values there are.
The median is the middle value once the data is in order.
The mode is the value that appears most often; the range is highest minus lowest.
Standard deviation measures how spread out the values are around the mean.
Quartiles split ordered data into four equal parts; the interquartile range is the middle half.
A high standard deviation means unpredictable data, which makes planning harder.
Statistics support analysis — use them to make comparisons, not as decoration.
Mean, median, mode and range
All four describe the same data differently, and the right one depends on the question. The mean uses every value, which is its strength and its weakness: one extreme figure drags it off.
Notice the mode, 92, appears three times. For a manager deciding how many staff to roster, that is arguably the most useful number of the four.
WE 1
Find the mean, median, mode and range
Case study: Corvo Kitchen recorded covers served on seven consecutive nights: 84, 92, 76, 92, 88, 92, 71.
Calculate the mean, median, mode and range of covers served. [6]
Mean — add the values, then divide84 + 92 + 76 + 92 + 88 + 92 + 71 = 595595 ÷ 7Mean = 85 coversMedian — put the data in order first
71, 76, 84, 88, 92, 92, 92 — the 4th of 7 values
Median = 88 coversMode and range
92 appears three times; 92 − 71 = 21Mode = 92, range = 21reorder the data before finding the median. Every year students take the middle of the unsorted list.
Standard deviation: the spread
Two data sets can share a mean and behave completely differently. Standard deviation is the number that tells them apart, and for a manager it is really a measure of how predictable the business is.
Shop B’s manager has to choose between overstocking most weeks or running out in the busy ones. Shop A’s manager does not.
WE 2
Calculate a standard deviation
Case study: Pellow Ltd sells five products. Last month’s sales, in $000s, were: 50, 20, 40, 10, 30.
Calculate the standard deviation of last month’s sales. [4]
Step 1 — find the mean(50 + 20 + 40 + 10 + 30) ÷ 5 = 150 ÷ 5 = 30Step 2 — subtract the mean and square each result20² = 400, (−10)² = 100, 10² = 100, (−20)² = 400, 0² = 0Step 3 — add them and divide by how many values400 + 100 + 100 + 400 + 0 = 1,000, then 1,000 ÷ 5 = 200Step 4 — take the square root√200 = 14.14…Standard deviation ≈ 14.1 ($000s)a spread of about $14,100 around a $30,000 mean is large. Pellow’s sales are not predictable.
Quartiles and the interquartile range
Quartiles cut ordered data into four equal groups. The top quartile is the highest 25%, and the interquartile range is the middle half — useful because it ignores the extremes at both ends.
WE 3
Identify the top quartile
Case study: Halden Tools pays a bonus to salespeople in the top quartile. Twelve salespeople recorded sales of: 24,100 / 31,500 / 19,400 / 26,300 / 22,300 / 28,900 / 18,200 / 25,750 / 30,200 / 21,050 / 27,400 / 23,600.
Identify the salespeople who should receive a bonus. [4]
Step 1 — put the data in order, smallest to largest
18,200 / 19,400 / 21,050 / 22,300 / 23,600 / 24,100 / 25,750 / 26,300 / 27,400 / 28,900 / 30,200 / 31,500
Step 2 — split into four equal groups12 ÷ 4 = 3 salespeople per quartileStep 3 — take the highest groupTop quartile: 28,900 / 30,200 / 31,500the three highest sellers get the bonus. Ordering the list is where the marks are.
Charts, and choosing the right one
Type
Best for
Watch out for
Bar chart
Comparing separate items, such as sales per store
An axis that does not start at zero exaggerates differences
Line graph
Showing a trend over time
A short time period can make a blip look like a trend
Pie chart
Showing how a whole splits into parts
Percentages hide the size of the whole — 40% of what?
Infographic
Communicating a few headline figures quickly
Designed to persuade, so check the source
Turn a percentage into a value. If a pie chart says a product is 23% of sales and total sales were $180,000, the answer is 0.23 × $180,000 = $41,400. That two-step move appears constantly in 2-mark calculate questions.
You do not have to wait to be told to use statistics. Working out a percentage change or comparing two means inside a 10-mark answer is exactly the kind of application that lifts a response into the top band.
💡 Exam tip
Order the data first for median and quartile questions. Always.
Show every step. The method marks are given for the working, not the final number.
Keep the units. If the data is in $000s, say so in your answer.
Interpret the number. “The standard deviation is 14.1” is a calculation; “so sales are unpredictable, making stock planning hard” is analysis.
Comment on the sample when data comes from a survey — how many replied, and were they representative?
Compare two figures where you can. Statistics earn most marks when used to support a comparison.
⚠ Common mix-up
Taking the median from an unordered list. The middle of the list is not the median until it is sorted.
Forgetting the square root at the end of a standard deviation. Stopping at the variance is a lost mark.
Confusing range with standard deviation. Range uses two values; standard deviation uses all of them.
Assuming the mean is a typical value. One extreme figure pulls it away from reality.
Quoting a statistic without saying what it means for the business.
Trusting a chart’s axis. A truncated axis makes small differences look dramatic.
Up next: Circular Business Models — the last tool in the kit, and the one about what happens to a product after the customer has finished with it.
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