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Quartiles in data analysis are measures that divide a dataset into four equal parts, representing key percentiles. They help identify the spread, central tendency, and shape of data, and are essential for detecting outliers and summarizing large datasets. The interquartile range (IQR) and quartile deviation provide robust measures of dispersion, while box plots visually depict data distribution.

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## Definition of Quartiles

### Statistical values that divide a ranked dataset into four equal parts

Quartiles are crucial for describing the spread, central tendency, and shape of data

### Calculation of Quartiles

First Quartile (Q1)

Q1 is the 25th percentile and indicates that 25% of the data is below this value

Second Quartile (Q2)

Q2 is the median and divides the dataset into two equal halves

Third Quartile (Q3)

Q3 is the 75th percentile and shows that 75% of the data is below this value

### Importance of Quartiles

Quartiles are vital for identifying the spread, central tendency, and shape of a dataset, and are particularly helpful for detecting outliers and understanding the distribution of the data

## Interquartile Range (IQR)

### Definition of IQR

IQR is the difference between the third and first quartiles and quantifies the dispersion of the middle 50% of the data

### Quartile Deviation

Quartile deviation, or semi-interquartile range, is half of the IQR and serves as a measure of dispersion around the median

### Robustness of IQR and Quartile Deviation

These metrics are more reliable measures of dispersion than range or standard deviation as they are less affected by extreme values

## Box Plots

### Definition of Box Plots

Box plots, or box-and-whisker diagrams, are graphical tools that utilize quartiles to depict the distribution of a dataset

### Components of Box Plots

Box

The box extends from Q1 to Q3 and represents the middle 50% of the data

Median Line

The median line represents Q2, the value that divides the dataset into two equal parts

Whiskers

The whiskers reach out to the smallest and largest values, excluding outliers

### Uses of Box Plots

Box plots offer a visual summary of the data's central tendency, variability, and potential outliers, facilitating exploratory data analysis

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