Mean, Median, Mode, and Weighted Mean
Choose the summary that matches the data—and keep totals and weights visible.
Mean, Median, Mode, and Weighted Mean
Not yet verified on this browser.
The measures answer different questions
Mean is total divided by count. Median is the middle after ordering. Mode is most frequent. A weighted mean multiplies each value by its share before adding.
weighted mean = Σ(value×weight)/ΣweightsMean follows the total
If the mean and number of observations are known, total = mean×count.
Median resists outliers
An extreme value can pull the mean while leaving the middle position nearly unchanged.
Write total = mean × count
For a missing score, find the target total first. Mean 18 for 4 values means total 72. If three values total 49, the missing value is 23.
Why it works
Mean problems become ordinary total problems once you recover the sum.
Five forms you should recognize
Problem: A player scored 6, 8, 9, 12, and 15 points in five games. What was the mean score?
(6 + 8 + 9 + 12 + 15)5 = 10Why: The mean distributes the total of 50 equally across five games.
Problem: Find the median of 11, 4, 9, 7, and 15.
4, 7, 9, 11, 15 → median = 9Why: Median means the middle position after ordering the values.
Problem: What is the mode of 3, 5, 5, 6, 8, 8, 8, and 9?
mode = 8Why: Eight occurs three times, more frequently than any other value.
Problem: Quizzes count 40% and the exam 60%. A student earned 85 in quizzes and 90 on the exam. What is the final grade?
0.40(85) + 0.60(90) = 88Why: Multiply each score by its contribution before adding.
Problem: Ten students have mean 80 and fifteen students have mean 90. What is their combined mean?
[10(80) + 15(90)]25 = 86Why: Recover both group totals first; directly averaging 80 and 90 would ignore the different group sizes.
Check before you commit
- Finding a median before ordering
- Dividing a weighted total by the number of categories
- Averaging group means without group sizes
- Calling the largest value the mode
- Ignoring an outlier
- Rounding before the final step
Do you need the lesson-or just practice?
One original question in each form recommends your next step. It does not yet verify mastery.
Work at the level you need.
Foundations
Build the core procedure with immediate explanations.
Core Practice
Use mixed forms with less scaffolding.
UPCAT-Style Transfer
Apply the competency in unfamiliar representations.
Ready to verify this competency?
A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.
Mean, Median, Mode, and Weighted Mean FAQ
Can there be more than one mode?
Yes. Two values tied for highest frequency make the set bimodal.
When is median better than mean?
When the distribution is skewed or contains extreme outliers.
Do weights need to total 100%?
They must share a common total; percentages usually total 100%.
Continue your mathematics review.
Your progress stays on this browser.
Mastery results save to your Teacher Abi study profile.
Return to Student Hub View UPCAT Coverage
No comments:
Post a Comment