neljännesarvoihin

Neljännesarvoihin, which translates to "quartiles" in English, are a set of values that divide a dataset into four equal parts. They are a common tool in statistics for understanding the distribution of data. The three main quartiles are the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3).

The first quartile (Q1) is the value below which 25% of the data falls. It is also known as the lower quartile. The second quartile (Q2) is the median of the dataset, meaning 50% of the data falls below it and 50% falls above it. The third quartile (Q3) is the value below which 75% of the data falls. It is also known as the upper quartile.

To calculate quartiles, the data must first be ordered from least to greatest. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values. Q1 is the median of the lower half of the data (excluding the overall median if the dataset has an odd number of points), and Q3 is the median of the upper half of the data (again, excluding the overall median if applicable).

Quartiles are useful for identifying the spread and central tendency of data. The interquartile range (IQR), which is the difference between Q3 and Q1 (IQR = Q3 - Q1), provides a measure of the variability of the middle 50% of the data. This range is less affected by outliers than the total range of the data. Quartiles are often used in box plots to visually represent data distribution, showing the median, quartiles, and potential outliers.