Math Problem Statement

what is the minimum, first quartile, median, third quartile, and max of these numbers 4.1, 5.2, 5.2, 6.0, 6.2, 6.3, 6.5

Solution

To find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum for the given data set:
4.1, 5.2, 5.2, 6.0, 6.2, 6.3, 6.5, we follow these steps:

Step 1: Arrange the numbers in ascending order (already done):

4.1, 5.2, 5.2, 6.0, 6.2, 6.3, 6.5

Step 2: Calculate the values:

  1. Minimum: The smallest number in the data set is 4.1.

  2. First Quartile (Q1): Q1 is the median of the lower half of the data (below the median). In this case:

    • The lower half of the data is 4.1, 5.2, 5.2.
    • The median of this subset is 5.2 (since it's the middle number).
  3. Median (Q2): Q2 is the middle value of the entire data set. Since there are 7 numbers, the median is the fourth value:

    • The median is 6.0.
  4. Third Quartile (Q3): Q3 is the median of the upper half of the data (above the median). The upper half is 6.2, 6.3, 6.5.

    • The median of this subset is 6.3.
  5. Maximum: The largest number in the data set is 6.5.

Final Summary:

  • Minimum: 4.1
  • First Quartile (Q1): 5.2
  • Median (Q2): 6.0
  • Third Quartile (Q3): 6.3
  • Maximum: 6.5

Would you like more details on how quartiles are calculated, or any other clarification?

5 Related Questions:

  1. What is the interquartile range (IQR) of this data set?
  2. How can quartiles be used to detect outliers?
  3. What would happen if we added another number to this data set? How would the quartiles change?
  4. How do quartiles differ from percentiles in terms of interpretation?
  5. Can quartiles be used in analyzing real-world data, such as income distribution?

Tip: Quartiles divide data into four equal parts and are useful for understanding the spread and central tendency of a data set.

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Math Problem Analysis

Mathematical Concepts

Statistics
Quartiles
Descriptive Statistics

Formulas

Minimum: The smallest value in the data set
First Quartile (Q1): Median of the lower half of the data
Median (Q2): Middle value of the data set
Third Quartile (Q3): Median of the upper half of the data
Maximum: The largest value in the data set

Theorems

Quartiles divide a data set into four equal parts

Suitable Grade Level

Grades 8-10