Pariksha SaathiMean, Median and Mode Questions with Solutions
These are three different ways to describe "the typical value" of a data set, and each needs its own method — mean needs a sum, median needs sorting, mode needs counting. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- Mean (the ordinary average) = sum of all values / number of values.
- Median = the middle value once the data is SORTED. With an odd count, it’s the single middle value; with an even count, it’s the average of the two middle values.
- Mode = the value that occurs most often. A data set can have one mode, more than one (if there’s a tie), or none at all (if every value is equally frequent).
- Always sort the data first before finding the median — trying to spot the middle value in unsorted data is the most common source of errors in this topic.
Worked examples
1. Find the median of: 12, 7, 15, 9, 21, 7, 18
Solution
- Sort the data: 7, 7, 9, 12, 15, 18, 21 — 7 values, so the median is the 4th value.
- The 4th value is 12.
Answer: 12
2. Find the mode of: 4, 8, 4, 6, 8, 4, 9
Solution
- Counting occurrences: 4 appears 3 times, 8 appears 2 times, 6 and 9 appear once each.
- The most frequent value is 4.
Answer: 4
3. The marks of 6 students are: 45, 60, 55, 70, 65, 50. Find the median.
Solution
- Sort the data: 45, 50, 55, 60, 65, 70 — 6 values (even), so the median is the average of the 3rd and 4th values.
- Median = (55 + 60) / 2 = 57.5.
Answer: 57.5
4. Find the mean, median and mode of the data set: 10, 15, 10, 20, 15, 10, 25
Solution
- Mean: sum = 10+15+10+20+15+10+25 = 105, and 105 / 7 = 15.
- Median: sorted data is 10, 10, 10, 15, 15, 20, 25 — the 4th (middle) value is 15.
- Mode: 10 appears 3 times, more than any other value, so the mode is 10.
Answer: Mean = 15, Median = 15, Mode = 10
Try these yourself
Sort the data first for median, then count for mode, and check against the answer.
1. Find the median of: 8, 3, 11, 5, 14, 3, 9
Answer: 8
2. Find the mode of: 6, 9, 6, 7, 9, 6, 11
Answer: 6
3. Find the mean, median and mode of: 12, 18, 12, 24, 18, 12, 30
Answer: Mean = 18, Median = 18, Mode = 12
Where this comes up
Mean, Median and Mode is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and often appears alongside Data Interpretation.
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