Mathematics
Grade 6
15 min
Quartiles
Quartiles
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1
Introduction & Learning Objectives
Learning Objectives
Define what quartiles are and their purpose.
Correctly order a given set of numerical data.
Identify and calculate the median (second quartile, Q2) of a data set.
Identify and calculate the first quartile (Q1) of a data set.
Identify and calculate the third quartile (Q3) of a data set.
Interpret the meaning of Q1, Q2, and Q3 in simple data contexts.
Have you ever wondered how to split a list of numbers into four equal groups? 🤔 Today, we'll learn about 'quartiles' – a cool way to understand how data is spread out!
In this lesson, you will discover what quartiles are and how to find them. Quartiles help us divide a set of numbers into four equal sections, giving us a clearer picture of the data's distribution. This skill is super usef...
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Key Concepts & Vocabulary
TermDefinitionExample
Data SetA collection of numbers or information gathered for a specific purpose.The ages of students in a club: {10, 11, 9, 10, 12}
Ordered DataA data set where the numbers are arranged from the smallest value to the largest value.If the data set is {10, 11, 9, 10, 12}, the ordered data is {9, 10, 10, 11, 12}.
Median (Q2)The middle value of an ordered data set. If there are two middle values, it's their average.For {9, 10, 10, 11, 12}, the median (Q2) is 10.
QuartilesValues that divide an ordered data set into four equal parts, each containing 25% of the data.Q1, Q2 (Median), and Q3 are the three quartiles.
First Quartile (Q1)The median of the lower half of an ordered data set. It marks the point below which 25% of the data falls.For {9, 10, 10, 11, 12}, the lowe...
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Core Formulas
Rule 1: Order the Data
Always arrange your data set from the smallest number to the largest number.
This is the very first and most important step for finding quartiles. Without ordered data, your calculations will be incorrect.
Rule 2: Find the Median (Q2)
The median ($Q_2$) is the middle value of the ordered data set.
- If there's an odd number of data points, $Q_2$ is the single middle number.
- If there's an even number of data points, $Q_2$ is the average of the two middle numbers: $Q_2 = \frac{\text{middle value 1} + \text{middle value 2}}{2}$.
The median divides the data into two equal halves. This is your second quartile.
Rule 3: Find the First Quartile (Q1)
The first quartile ($Q_1$) is the median of the lower half of the data. The lower half inclu...
4 more steps in this tutorial
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Challenging
The data set {10, 15, 20, 25, 30} has a median (Q2) of 20. If a new number, 5, is added to the set, what is the new median (Q2)?
A.17.5
B.15
C.20
D.12.5
Challenging
An ordered data set has 7 numbers. The third quartile (Q3) is 22. Which of the following MUST be true?
A.The largest number is 22.
B.The median of the data set is 22.
C.At least two numbers in the set are larger than 22.
D.The 6th number in the ordered set is 22.
Challenging
The quartiles for a data set are Q1=10, Q2=15, and Q3=20. Which of the following data sets could this represent?
A.{10, 12, 15, 18, 20}
B.{5, 10, 15, 20, 25}
C.{8, 10, 12, 15, 18, 20, 22}
D.{10, 15, 20, 25, 30, 35, 40}
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