Mathematics and Statistics · Ch 10 — Partition Values
Partition Values — The Idea of Position
Partition Values — The Idea of Position
The median of a set of data is the middle value: it splits an ordered data set into two equal halves, with as many observations below it as above it. Partition values extend exactly this idea — they are the values that divide an ordered data set into a chosen number of equal parts.
This chapter of the Maharashtra Std XI (FYJC) commerce Mathematics and Statistics course studies three families of partition values:
The Three Families
- Quartiles — three values that divide the data into 4 equal parts.
- Deciles — nine values that divide the data into 10 equal parts.
- Percentiles — ninety-nine values that divide the data into 100 equal parts.
These are the same partition-value (positional-average) principles set out in the national mathematics/statistics curriculum, and they are used throughout commerce and economics to describe where a value stands within a distribution — for example, the income level below which the poorest 25% of households fall, or the marks separating the top 10% of candidates.
Always Arrange the Data First
Every partition value is a positional average — it is read off the data in order. So the very first step, for every method in this chapter, is to arrange the raw values in ascending order, or (for a frequency distribution) to build the less-than cumulative frequency column. Skipping this step is the single most common source of a wrong answer.
Because the median already splits the data in half, it coincides with the middle members of all three families. This central identity is worth memorising from the start:
A value that divides an ordered data set into a given number of equal parts. Quartiles give 4 parts, deciles 10 parts, and percentiles 100 parts.
Quartiles (4 parts); deciles (10 parts); percentiles (100 parts). The middle of each equals the median: .