Q.14 Calculate the value of median from the given data:
2.90, 3.57, 3.73, 2.98, 3.64, 3.75
3.30, 3.62, 3.76, 3.38, 3.66, 3.76
1. 3.505
2. 3.62
3. 3.63
4. 3.65
Median Calculation: Sorted Data Value 3.63
The median for even-numbered datasets is the average of the two central values after sorting. For the given data, the correct answer is 3.63.
Step-by-Step Calculation
Arrange the 12 values in ascending order: 2.90, 2.98, 3.30, 3.38, 3.57, 3.62, 3.64, 3.66, 3.73, 3.75, 3.76, 3.76. For n=12 (even), the median is the average of the 6th (3.62) and 7th (3.64) values: (3.62 + 3.64)/2 = 7.26/2 = 3.63.
Option Explanations
1. 3.505 (Incorrect)
This value approximates an unrelated statistic, possibly a miscalculated mean or lower quartile, not matching the central tendency formula for even datasets.
2. 3.62 (Incorrect)
3.62 is the 6th ordered value, one of the two middle numbers, but the median requires averaging it with the 7th value (3.64).
3. 3.63 (Correct)
Precisely (3.62 + 3.64)/2 = 3.63, the standard median for this even-sized, sorted dataset, robust against outliers.
4. 3.65 (Incorrect)
3.65 exceeds the true average of central values; it might stem from rounding errors or averaging incorrect positions like 7th and 8th.
