Theory
Three honest answers, one question
The CampusPulse survey's screen-time column for seven hostellers, in minutes:
60, 90, 90, 120, 150, 180, 600
(The 600 is real: one student watched a full cricket match.)
"What is the typical screen time?" Mean says 184.3. Median says 120. Mode says 90. Three defensible answers to one question, and the marks in this topic come from computing each correctly AND knowing which to report.
Theory
Three committee members
Ask a committee where the class "centre" is:
- The accountant totals everything and divides: precise, but one extreme member skews the report.
- The middle-finder sorts everyone and points at the central person: extremes cannot move them.
- The popularity-counter names whatever occurs most: the only member who can also handle labels (most common city).
You met this committee in BCA303 with pandas doing the arithmetic. Today the exam wants it by hand, with reasons.
Theory
Computing each, precisely
Data: 60, 90, 90, 120, 150, 180, 600 (n = 7, already sorted).
Mean = sum ÷ n = 1290 ÷ 7 ≈ 184.3 min.
Median = value at position (n+1)/2 = 4th value = 120. (SORT FIRST, always. Even n? Average the two middle values.)
Mode = most frequent = 90 (appears twice).
Notice the spread of answers: the 600 dragged the mean above six of the seven students. The median never felt it.
At a glance
Merits and demerits (the 5-mark table)
| Measure | Strengths | Weaknesses |
|---|---|---|
| Mean | Uses every value; algebra-friendly | Distorted by outliers; numeric only |
| Median | Outlier-proof; works for ordinal data | Ignores exact magnitudes |
| Mode | Only choice for nominal data; a real observed value | May be none, or several; can be unrepresentative |
Think first
Work one with an even n
Commute minutes of 6 students: 25, 10, 40, 20, 30, 15. On paper: sort, then find the median (careful: n is even), the mean, and the mode. Then tap.
Show the answer
Sorted: 10, 15, 20, 25, 30, 40.
Median: n = 6 is even, so average the 3rd and 4th values: (20 + 25) / 2 = 22.5.
Mean: 140 ÷ 6 ≈ 23.3.
Mode: every value appears once: no mode.
Two traps dodged: the even-n averaging step, and the honest answer "no mode" (data does not owe you one). Mean ≈ median here: no outlier, symmetric-ish data, both centres agree.
Quiz
A report on hostel screen time must state ONE typical value. Given the 600-minute outlier, which measure and which justification earn full marks?
- Median 120, because the median resists outliers that distort the mean in skewed data
- Mean 184.3, because the mean uses every observation and is therefore always best
- Mode 90, because the mode is always the safest choice
- Any of them, since all three are measures of central tendency
Show the answer
Median 120, because the median resists outliers that distort the mean in skewed data
Skewed data with an outlier is EXACTLY the median's home ground: it reports where the bulk of students actually sit, while the mean was dragged to a value above six of seven observations. Option B's justification is real (the mean does use every value) but that very property is its weakness here. "Always" and "any" answers (C, D) surrender the judgement the question is testing.
Watch out
Where the marks leak
Unsorted median: the middle of raw data is a random number. Sort, then count to position (n+1)/2.
Even n: forgetting to average the two middle values.
Skew signature: if mean > median noticeably, the data is right-skewed (a long tail of large values): stating this one-line diagnosis next to your numbers upgrades an answer from computed to understood.
Theory
Where each measure runs the real world
Median: house prices and salaries (one crorepati should not define "typical"). Mean: exam marks, cricket averages, anything roughly symmetric. Mode: shoe sizes a shop stocks, most common blood group in a blood bank. In BCA303 you computed these in pandas; Unit 5 of THIS subject does it in R (with a surprise: R has no built-in mode function). The concepts stay identical across all three.
Summary
Key takeaways
- Mean = sum/n: uses everything, bends to outliers.
- Median = middle of SORTED data, position (n+1)/2; even n averages the two middles; outlier-proof.
- Mode = most frequent: can be none, one, or several; the only measure for nominal data.
- Skewed data or outliers → report the median; symmetric numeric data → mean; labels → mode.
- Mean noticeably above median = right skew (long tail of big values).
- Memory hook: accountant, middle-finder, popularity-counter: pick the right committee member.