A reliable method
For means, recover the total with count × mean. For medians, sort first; for a range, subtract the minimum from the maximum.
The common trap
A large sample does not fix biased sampling. Random sampling and random assignment answer different questions.
Make the connection
Adding a constant to every observation shifts the mean and median by that constant but leaves the range unchanged.
Recover totals before combining means
Four observations with mean 6 have total 24. Adding an observation of 16 gives a total of 40 across five observations, so the new mean is 8. Averaging 6 and 16 gives 11 and weights the four-item group as if it contained one observation. Count matters when combining means.
Compare shift and scale
For data 2,4,9, the mean is 5, median is 4 and range is 7. Adding 3 gives 5,7,12: mean 8, median 7, range still 7. Multiplying by 3 gives 6,12,27: mean 15, median 12, range 21. Location and spread respond differently to addition, but both change under positive scaling.
Try, then check
For data 1,2,3,4,40, the median is 3 and the mean is 10. Replacing 40 with 100 leaves the median unchanged and makes the mean 22. Explain this using order for the median and total for the mean. A large sample alone does not protect either statistic from biased collection.
The mean of 3 numbers is 4. What is their sum?
- Mean = sum / number of observations.
- Multiply the mean 4 by the count 3.
- The sum is 12.
Compare the other answer choices
Reported the mean rather than the total.
Added count and mean.
Divided mean by count instead of multiplying.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Official mathematics skillsSiyavula Grade 10 mathematics