Medidas descriptivas

Quartiles

The values that divide the data set into 4 equal parts after it has been arranged in ascending orden are called quartiles.

Split into quartes the following set of data:

2 1 3 2 1 1 2 3 1 4 3 1

Step 1. Rearrange the value in ascending order:

1 1 1 1 1 2 2 2 3 3 3

Step 2. Split into quartes:

This are the same data as before, but this tim eit's split into quartes:

The quartiles are:

Q₁ , the lowest quartile is known as the lower quartile, or first quartile. The lowest 25% of the data being found below the first quartile value. It is the same as P₂₅.
Q₂ , the quartile in the middle is known as the median. The lowest 50% of the data set should be found below the second quartile. It is the same as the median, D₅ and P₅₀.
Q₃ , the highest quartile is known as the upper quartile. The lowest 75% of the data set should be found below the third quartile. It is the same as P₇₅.

Steps to find quartile values on a data set with n elements:

Step 1. Calculate: and round to the nearest integer. If L falls halfway between two integers, round up. The Lth element is the lower quartile value.

Step 2. Calculate: and round to the nearest integer. If U falls halfway between two integers, round down. The Uth element is the upper quartile value.

Find the quartiles of the data set: {1, 3, 4, 5, 5, 6, 9, 14, 21}

Step 1. n = 9, so which becomes 3 after rounding up. The lower quartile value is the 3rd data point, Q₁=4.
Step 2. which becomes 7 after rounding down. The upper quartile value is the 7th data point, Q₃ =9. Using this method, the upper and lower quartile values are always two of the data points.
Step 3. Q₂=5, because the median is 5.

There is another way to find the quartiles: Turkey's method:

Divide the set into four equal parts (by Turkey's method):

{6, 3, 4, 9, 6, 2, 7, 7, 8, 4, 10}

Step 1. Arrange your data in ascending order:

2, 3, 4, 4, 6, 6, 7, 7, 8, 9, 10

Step 2. Find the median of the data set.

This is Q₂=6

Step 3. Find the median of the lower half of the data set (in parenthesis)

(2, 3, 4, 4, 6), 6, 7, 7, 8, 9, 10
This is Q₁=4.

Step 4. Find the median of the upper half of the data set (in parenthesis)

2, 3, 4, 4, 6, 6, (7, 7, 8, 9, 10)
This is Q₃=8

Quartiles for grouped data.
The formulae for calculating Q₁, Q₂ and Q₃ for grouped data are:

where:

is the lower limit of interval (or class) containing
is the frequency of the interval containing
w is the width of the interval containing
cf is the cumulative frequency up to, but not including the interval.

Find Q₁ from these grouped data:

Class Limit	Frequency	Cumulative frequency
0-10	2	2
10-20	3	5
20-30	5	10
30-40	2	12
40-50	6	18
50-60	2	20

N/4=5