The median value of the following data: 1, 2, 3, 5, 8 and 100 is

Correct option is C

Introduction
· The median is a fundamental measure of central tendency in biostatistics that identifies the precise middle point of a data distribution.
· In environmental studies, the median is frequently used to describe datasets that contain extreme outliers, such as heavy metal concentrations or noise levels, where the mean might be misleading.
· It effectively divides a sample into two equal halves, ensuring that 50% of the observations fall below the median and 50% fall above it.

Information Booster

Sol. To calculate the median for the given dataset: $1, 2, 3, 5, 8, 100:
1. Arrange the data: The values must be in ascending or descending order. The given sequence is already in ascending order: 1, 2, 3, 5, 8, 100.
2. Determine the number of observations (n): Here, n = 6.
3. Apply the Median Formula: Since $n$ is an even number (6), the median is the arithmetic average of the two middle-most terms.
· Lower middle term ($$n/2): 6/2 = 3^{rd}$$​term.
· Upper middle term ($$n/2 + 1): 3 + 1 = 4^{th}$$​term
Calculate the average: The 3^rd term is 3 and the 4^th term is 5.
· Median =$$\frac{3 + 5}{2} = \frac{8}{2} = 4$$.
· The median is highly "resistant" or "robust" against outliers; in this dataset, the value 100 is a significant outlier that would pull the mean to $19.83$, but the median remains a stable 4.
· For any dataset with an odd number of observations (n), the median is simply the value at the position $$\frac{n+1}{2}$$​.
· In a frequency distribution curve, the median is the value on the X-axis where a vertical line divides the total area under the curve into two equal parts.
· The median is also synonymous with the 2^nd Quartile (Q_2) or the 50^th Percentile of a cumulative frequency distribution.
· It is the preferred measure of central tendency for "ordinal" data or highly skewed "interval" data commonly found in ecological sampling.