First quartile

Definition

The first quartile (Q1) is the value that separates the lowest 25% of the data set from the rest. It is also known as the 25th percentile.

5 Must Know Facts For Your Next Test

1. The first quartile can be found using the formula Q1 = (n+1)/4, where n is the number of observations in the data set.
2. Q1 is used to identify outliers; values below Q1 - 1.5*IQR are considered outliers.
3. It is one of three quartiles, including Q2 (median) and Q3 (third quartile).
4. Q1 helps in understanding the spread and distribution of the lower part of a data set.
5. In a box plot, Q1 marks the left boundary of the box.

Review Questions

• How do you calculate the first quartile for a given data set?
• What role does Q1 play in identifying outliers?
• Where is Q1 represented in a box plot?

Related terms

Median: The median (Q2) is the middle value that separates the higher half from the lower half of a data set.

Interquartile Range (IQR): The IQR is calculated as Q3 - Q1 and measures the spread of the middle 50% of a data set.

Third Quartile: $Q3$ or third quartile, represents the value separating the highest 25% from the rest of a data set, also known as the 75th percentile.