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🎲intro to statistics review

Third Quartile

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The third quartile, also known as the 75th percentile, is a measure of the location of data that divides the data set into four equal parts. It represents the value below which 75% of the data points fall.

5 Must Know Facts For Your Next Test

  1. The third quartile (Q3) is the value that separates the upper 25% of the data from the lower 75% of the data.
  2. The third quartile is an important measure of the location of data, as it provides information about the distribution and spread of the data.
  3. The third quartile is a key component of the box plot, a graphical representation of the five-number summary (minimum, Q1, median, Q3, and maximum).
  4. The third quartile can be used to identify outliers in a data set, as values that fall outside the range of Q1 - 1.5 * IQR to Q3 + 1.5 * IQR are considered potential outliers.
  5. The third quartile, along with the first quartile and median, can be used to calculate the interquartile range (IQR), which is a measure of the spread of the middle 50% of the data.

Review Questions

  • Explain the relationship between the third quartile and the overall distribution of a data set.
    • The third quartile (Q3) is the value that divides the data set into four equal parts, with 75% of the data falling below this value. This means that the third quartile provides important information about the location and spread of the data. It can be used to identify the upper boundary of the middle 50% of the data, as well as potential outliers in the upper end of the distribution. Understanding the third quartile in the context of the overall data set is crucial for interpreting the distribution and making informed decisions based on the data.
  • Describe how the third quartile is used in the construction and interpretation of a box plot.
    • The third quartile (Q3) is a key component of the box plot, a graphical representation of the five-number summary (minimum, first quartile, median, third quartile, and maximum). The third quartile is used to define the upper boundary of the box in the box plot, with the box itself representing the middle 50% of the data (the interquartile range). The position of the third quartile relative to the other quartiles and the median provides valuable information about the symmetry, skewness, and overall spread of the data distribution. Analyzing the third quartile in the context of the box plot can help identify outliers and gain a deeper understanding of the data set.
  • Evaluate the importance of the third quartile in the calculation and interpretation of the interquartile range (IQR), and explain how this measure of spread can be used to identify potential outliers in a data set.
    • The third quartile (Q3) is a crucial component in the calculation of the interquartile range (IQR), which is the difference between the third quartile and the first quartile (Q3 - Q1). The IQR provides a measure of the spread or variability of the middle 50% of the data, and it is often used to identify potential outliers in a data set. Specifically, values that fall outside the range of Q1 - 1.5 * IQR to Q3 + 1.5 * IQR are considered potential outliers. By understanding the relationship between the third quartile and the IQR, you can effectively evaluate the distribution of the data, identify unusual or extreme observations, and make more informed decisions based on the data.

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