Question
The marks obtained by 10 students in a test are: 12, 15, 15, 18, 20, 22, 25, 28, 30, 95. Find the mean, median, and mode. Which measure best represents this data, and why?
Solution — Step by Step
Data is already sorted. With 10 values (even count), median is the average of the 5th and 6th values:
The value 15 appears twice (most frequent). Mode = 15.
The mean (28) is pulled up by the outlier (95). Most students scored between 12-30, so 28 is misleadingly high. The mode (15) only reflects the most common score, not the centre. The median (21) is the best representative here — it is unaffected by the extreme value 95.
graph TD
A["Which central tendency to use?"] --> B["Is data symmetric, no outliers?"]
B -->|Yes| C["Use MEAN - most informative"]
B -->|No| D["Are there outliers or skewed data?"]
D -->|Yes| E["Use MEDIAN - resistant to outliers"]
A --> F["Is data categorical like shoe sizes?"]
F -->|Yes| G["Use MODE - only option for categories"]Why This Works
The mean uses every data point, making it sensitive to outliers. One extremely high or low value can drag the mean away from the “typical” value. The median simply finds the middle position — no matter how extreme the outliers, the middle value stays put. The mode tells us the most popular value but says nothing about the overall distribution.
In real life: when news reports say “median household income” instead of “mean household income,” they are using median precisely because a few billionaires would skew the mean upward and misrepresent the typical household.
Alternative Method
For grouped data in CBSE Class 10, use these formulas:
- Mean (direct method):
- Median: where = lower limit of median class, = cumulative frequency before median class, = frequency of median class, = class width
- Mode:
The median formula is the most commonly tested in boards. Practice it with at least 5 different datasets.
Common Mistake
Forgetting to sort the data before finding the median. The median is the middle value of SORTED data. If you pick the middle value from unsorted data, you get a completely wrong answer. Always arrange data in ascending or descending order first. In grouped data, students sometimes pick the wrong median class by not computing the cumulative frequency correctly — double-check your cumulative frequency column.