Deciles and percentiles
Deciles and percentiles
Deciles split a large group, ordered by size, into ten equal groups, each holding 10% of the data.
That is how the news describes the incomes in a country: all the households (families, or people living alone) are ordered by their income and split into ten.
- The bottom decile (decile 1) – the 10% of households with the lowest income.
- The top decile (decile 10) – the 10% of households with the highest income.
The mean income of a household in each decile, net a month (example figures, rounded):
The income rises slowly from decile to decile, and jumps in the top decile: from 26.5 thousand ₪ to 42 thousand ₪.
Inequality of income is measured by a number: how many times the mean income in the top decile is that in the bottom decile.
In the example: – a household in the top decile brings in on average 10 times as much as a household in the bottom decile.
Each decile holds the same number of households, so a decile’s share of all income is its mean divided by the sum of the means of all the deciles.
- The sum of the means: thousand ₪.
- The top decile’s share: – about a quarter of all income, earned by a tenth of the households.
In a small group too, each decile is a tenth of the people.
A company has 40 workers, so each decile holds 4 workers.
The top decile is the four workers who earn the most.
Their pay, in shekels:
The mean pay in the top decile: ₪.
Percentiles split the ordered data into a hundred parts. A value at the -th percentile is greater than percent of the data.
- A baby’s weight at the 75th percentile: 75% of the babies of the same age weigh less.
- A psychometric score at the 80th percentile: 80% of the candidates scored lower. It does not mean the candidate answered 80% of the questions correctly.
Quartiles, deciles and percentiles are one idea with different splits:
- – the 25th percentile.
- The median – the 50th percentile, the border between decile 5 and decile 6.
- – the 75th percentile.
- The top decile – the data above the 90th percentile.
The mean income of a household in each decile in a town, in thousands of shekels a month:
| Decile | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Income | 3.5 | 6 | 8 | 10 | 12 | 14 | 17 | 20 | 25 | 38.5 |
How many times as large as the income in the bottom decile is the income in the top decile?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What percent of all the income in the town goes to the top decile?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A newspaper wrote: “The top decile earns 11 times as much as everyone else.” What is the mistake?
A chain of shops has 50 workers.
How many workers are there in each decile?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
The pay of the workers in the top decile, in shekels:
Work out the mean pay in the top decile.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Noa’s psychometric exam score is at the 85th percentile.
What percent of the candidates scored higher than her?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A friend of hers says: “Noa answered 85% of the questions correctly.” Is he right? Explain.
A baby girl of six months weighs 7.2 kg, which is the weight at the 40th percentile for her age.
Out of 1,000 babies aged six months, about how many weigh less than her?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Is her weight above the median or below it? Between which quartiles is it?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power