Quartiles
Also called: Lower quartile, Upper quartile · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 5 "Measures of Central Tendency"
Meaning
Quartiles are three values that divide ordered data into four equal parts.
- Q1, the lower quartile, has 25% of items below it. Q1 = size of the (N+1)/4-th item.
- Q2 has 50% of items below it. It is the median.
- Q3, the upper quartile, has 75% of items below it. Q3 = size of the 3(N+1)/4-th item.
Quartiles show how the data spread around the middle, not just where the centre lies. They belong to the family of partition values, along with deciles and percentiles.
Example
In NCERT's marks example, the first quartile works out to Q1 = 13.5 marks. So one-fourth of the students scored 13.5 marks or less.
Don't confuse with
- Quarters: a quarter usually means a three-month period, as in quarterly GDP or PLFS bulletins. Quartiles have nothing to do with time. They are positions in ordered data.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Weighted arithmetic mean
- Median
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class
- Relative position of mean, median and mode