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Statistics
 Introduction Central Tendency Measures Mean Geometric Mean Harmonic Mean Median Mode Measures of Dispersion Quartiles Deciles Percentiles Range Mean Deviation Variance Standard Deviation Coefficient of variation Exercises Measures of skewness and kurtosis Skewness Kurtosis Quiz

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:

1. 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.
2. 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.
3. 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