Q.32 The median value for the dataset (12, 10, 16, 8, 90, 50, 30, 24) is __________.

To find the median of the dataset (12, 10, 16, 8, 90, 50, 30, 24), first arrange the numbers in ascending order: 8, 10, 12, 16, 24, 30, 50, 90. With 8 values (even count), the median is the average of the 4th and 5th values: (16 + 24)/2 = 20. Thus, the median value is 20.

Step-by-Step Solution

• Arrange data in order: 8, 10, 12, 16, 24, 30, 50, 90
• Positions 4 and 5 are 16 and 24; average them for median: 20
• This follows the standard rule for even-sized datasets

Common Errors Explained

• Mistake: Using unordered data yields wrong middle (e.g., 41 from 50+30/2). Always sort first
• Mistake: Treating as odd count confuses position ((n/2)th vs. average of two)
• Mistake: Confusing with mean (sum=240/8=30) or mode (none repeat)

Introduction to Median Calculation

Finding the median value dataset (12, 10, 16, 8, 90, 50, 30, 24) is key for statistics in competitive exams like IIT JAM. The median resists outliers (e.g., 90 here), unlike mean. Sorted: 8, 10, 12, 16, 24, 30, 50, 90—median is 20.

Detailed Calculation Guide

1. Sort ascending: 8, 10, 12, 16, 24, 30, 50, 90
2. n=8 (even), so average (n/2)th=4th (16) and 5th (24): (16+24)/2=20
3. Verify: Outlier 90 skews mean to 30, but median stays central

Why Median Matters in Exams

Ideal for skewed data in biology/chemistry datasets during IIT JAM prep. Practice similar: for {4,7,3,8,6,2}, median=5.5. Avoid pitfalls like skipping sort.

Quick FAQ

Q: Median formula even n?
A: Average of n/2 and n/2+1 terms.

Final Answer: 20 for this dataset.