Median
Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 4 "Presentation of Data"; Class 11, Ch 5 "Measures of Central Tendency"; Class 11, Ch 8 "Use of Statistical Tools"
Meaning
The median is the middle value of data arranged in order. Half the items lie below it and half above. It depends on position, not on the size of every value, so a few very large or very small values do not pull it. This makes it the right average for skewed data such as income or monthly per capita consumption expenditure (MPCE).
- Ungrouped data: Median = size of the (N+1)/2-th item.
- Continuous data: Median = L + [(N/2 − c.f.)/f] × h. Here L is the lower limit of the median class, c.f. is the cumulative frequency of the classes before it, f is its frequency and h is its width.
The median can also be read from a graph: it is where the "less than" and "more than" ogives (cumulative frequency curves) cross. It is the same as the second quartile (Q2), the fifth decile (D5) and the 50th percentile (P50).
Example
NCERT's worked example on daily wages gives a median wage of Rs 35.83.
Don't confuse with
- Mode: the mode is the most frequent value and is read from a histogram. The median is the middle value and is read from the crossing point of the ogives.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Weighted arithmetic mean
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class
- Relative position of mean, median and mode