IB Business Management HLTopic 6 — The Business Management ToolkitPapers 1, 2 & 3Quantitative tool~11 min read
Working With Descriptive Statistics
Managers do not read raw data, they read summaries. Descriptive statistics turn a long list of numbers into three or four figures that actually mean something — the middle, the spread, and where the extremes sit.
📘 What you need to know
Mean = add everything up, divide by how many. Median = the middle value once sorted. Mode = the most common value.
Range = highest minus lowest. Quick, but one freak value ruins it.
Standard deviation measures how far the values sit from the mean. Small means consistent; large means unpredictable.
Quartiles cut a sorted list into four equal groups. The interquartile range is the middle half.
Two data sets can have the same mean and behave completely differently.
In the exam, always say what the number means for the business, not just what it is.
Averages: three different middles
Measure
How to find it
Best used when
Weakness
Mean
Total divided by the number of values
Values are fairly even
One huge value drags it away from reality
Median
Sort, then take the middle one
There are extreme values, such as house prices
Ignores the size of everything except the middle
Mode
The value that appears most often
Data are categories, such as shoe sizes
There may be two modes, or none at all
Even numbers of values? The median is the halfway point between the two middle numbers. With four boat prices of $390,000, $430,000, $450,000 and $520,000 the median is halfway between $430,000 and $450,000, which is $440,000.
Spread: the part people skip
The mean tells you the middle. It says nothing about how bumpy the numbers are, and bumpy is exactly what makes a business hard to run.
The business on the right needs far more spare cash, more flexible staffing and more storage, even though its average month looks identical.
Standard deviation, step by step
The four steps
1. Find the mean 2. Subtract the mean from each value and square it
3. Add the squares and divide by how many 4. Take the square root
WORKED EXAMPLE
Confirmed corporate bookings over five months were 300, 1,100, 1,500, 1,900 and 2,700. Calculate the standard deviation. [4 marks]
Step 1: mean300 + 1,100 + 1,500 + 1,900 + 2,700 = 7,5007,500 ÷ 5 = 1,500Step 2: subtract the mean, then square−1,200 → 1,440,000 −400 → 160,000 0 → 0400 → 160,000 1,200 → 1,440,000Step 3: add and divide by 53,200,000 ÷ 5 = 640,000Step 4: square root√640,000Standard deviation = 800 bookings800 on a mean of 1,500 is huge — say so, that is the application mark
Never stop at the number. A standard deviation of 800 against a mean of 1,500 means a typical month can swing by more than half the average. That is the sentence that turns a calculation into business analysis.
Quartiles and the middle half
The interquartile range is useful because it ignores the freak best month and the freak worst one, which the plain range does not.
WORKED EXAMPLE
A tour company received 200 reviews: 120 rated five stars, 40 four, 15 three, 10 two and 15 one. Calculate the mean rating to one decimal place. [2 marks]
Step 1: total the ratings(5 × 120) + (4 × 40) + (3 × 15) + (2 × 10) + (1 × 15)600 + 160 + 45 + 20 + 15 = 840Step 2: divide by the number of reviews840 ÷ 200 = 4.2Mean rating = 4.2 starsweighted mean: multiply each score by how many people gave it
WORKED EXAMPLE
Explain one advantage and one disadvantage to a small tour company of calculating the standard deviation of its monthly bookings. [4 marks]
Advantage, appliedIt shows how far a typical month sits from the average [1], so the owners can hold enough cash and staff to survive a 300-booking month rather than planning around the 1,500 average [1].Disadvantage, appliedIt is harder to calculate and interpret than a simple average [1], and a small family firm may have nobody with the training to use it properly without paying an adviser [1].4 marks“small business” is almost always the application hook for statistics questions
💡 Exam tips
Sort the list first for median, mode and quartiles. Most errors happen before any maths is done.
Show every step. Method marks survive an arithmetic slip.
Round only at the end, and to the number of places the question asks for.
Always add a sentence on what the figure means for planning: cash, staff, stock or pricing.
You can use statistics without being told to. Working out a mean from a case-study table is strong application.
For evaluation, question the sample: how many, chosen how, and when.
⚠ Common mix-ups
Assuming the mean is one of the original values. It usually is not.
Forgetting to sort before finding the median.
Dividing by the number of categories instead of the number of reviews in a weighted mean.
Skipping the squaring step in standard deviation, which makes the deviations cancel to zero.
Confusing range with standard deviation. Range uses two values; standard deviation uses them all.
Quoting a figure with no comment. A naked number scores the calculation mark and nothing else.
Up next: Circular Business Models — from numbers back to strategy, and a model that changes what a business does with its materials once customers have finished with them.
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