Q.3 Consider the following sample of numbers:
9, 18, 11, 14, 15, 17, 10, 69, 11, 13
The median of the sample is
(A) 13.5
(B) 14
(C) 11
(D) 18.7
Solved Example with 9, 18, 11, 14, 15, 17, 10, 69, 11, 13
Finding the median is a fundamental statistics skill for students, researchers, and anyone analyzing data sets. In this guide, we solve a multiple-choice question on the median of the sample 9, 18, 11, 14, 15, 17, 10, 69, 11, 13. We’ll walk through the exact steps, reveal the correct answer, and explain why each option is right or wrong.
What Is the Median?
The median is the middle value in a data set when numbers are arranged in ascending order. It resists outliers better than the mean, making it ideal for skewed data—like biology experiment results or population genetics samples.
For an even number of observations (here, 10), average the two middle values. For odd counts, pick the single middle one.
Step-by-Step: Calculating the Median for 9, 18, 11, 14, 15, 17, 10, 69, 11, 13
- List the raw data: 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 (n = 10, even).
- Sort in ascending order: 9, 10, 11, 11, 13, 14, 15, 17, 18, 69.
- Find middle positions: For n=10, positions are (10/2) = 5th and 6th values.
- Identify them: 5th = 13, 6th = 14.
- Average: (13 + 14)/2 = 27/2 = 13.5.
Wait—13.5? But let’s check the options. Hold on; I think I see a common mistake here. No, that’s correct math, but is this the answer? We’ll verify against options next.
Actually, upon double-check: Sorted list is correct: 9, 10, 11, 11, 13, 14, 15, 17, 18, 69. Yes, 5th=13, 6th=14, average=13.5.
Correct Answer and Full Explanation of Options
Correct Answer: (A) 13.5
This matches the standard median formula for even-sized samples. Outliers like 69 don’t skew it, unlike the mean (which is ~19.7 here).
Why Not the Other Options?
- (B) 14: Close, but incorrect. This assumes the median is just the 6th value (or rounding up). Beginners sometimes pick one middle value instead of averaging both. Always average for even n.
- (C) 11: Wrong. This is the 3rd/4th value—perhaps confusing with mode (11 appears twice) or lower quartile. Mode is 11, but question asks for median.
- (D) 18.7: Way off. This resembles the mean: sum=177, 177/10=17.7 (close to 18.7? Maybe a calc error like 187/10). Mean ≠ median here due to outlier 69.
| Option | Value | Why Incorrect (Except A) | Common Mistake |
|---|---|---|---|
| (A) | 13.5 | Correct | N/A |
| (B) | 14 | Single middle value | Forgetting to average |
| (C) | 11 | Mode or early position | Confusing median with mode |
| (D) | 18.7 | ~Mean | Using mean formula |
Tips for Median Calculations in Stats Exams or Research
- Always sort first—tools like Excel (MEDIAN function) or Python (numpy.median) automate this.
- Even n: Average nth/2 and (n/2)+1.
- Practice with biology data: E.g., median gene expression levels ignores extreme outliers.
Mastering median of the sample 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 builds intuition for real-world stats in genetics or plant sciences.
