Math Problem Statement

find the IQR of this data

Find the IQR of this data

Solution

To calculate the Interquartile Range (IQR) for the given data, we first need to list out the "Students" values:

  • 5, 6, 5, 16, 9, 4, 0, 2

The steps to calculate the IQR are as follows:

  1. Arrange the data in ascending order: 0,2,4,5,5,6,9,160, 2, 4, 5, 5, 6, 9, 16

  2. Find the median (Q2): Since there are 8 data points, the median is the average of the 4th and 5th values. These values are 5 and 5. Q2=5+52=5Q2 = \frac{5 + 5}{2} = 5

  3. Find the first quartile (Q1): This is the median of the lower half of the data (0, 2, 4, 5). The median of these four numbers is the average of the 2nd and 3rd values, which are 2 and 4. Q1=2+42=3Q1 = \frac{2 + 4}{2} = 3

  4. Find the third quartile (Q3): This is the median of the upper half of the data (5, 6, 9, 16). The median of these four numbers is the average of the 2nd and 3rd values, which are 6 and 9. Q3=6+92=7.5Q3 = \frac{6 + 9}{2} = 7.5

  5. Calculate the IQR: IQR=Q3Q1=7.53=4.5IQR = Q3 - Q1 = 7.5 - 3 = 4.5

Thus, the Interquartile Range (IQR) is 4.5.

Would you like more details or have any further questions about this process?

Here are some related questions for you:

  1. How would you calculate the mean and median for a set of data?
  2. What is the difference between range and interquartile range?
  3. How does the IQR help in identifying outliers in a data set?
  4. Can the IQR be used for both discrete and continuous data?
  5. How do you calculate the standard deviation for a data set?

Tip: When you have a small data set, such as this one, organizing the numbers from smallest to largest makes it easier to calculate the quartiles and IQR accurately.

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Math Problem Analysis

Mathematical Concepts

Statistics
Interquartile Range (IQR)
Data Organization
Quartiles

Formulas

Median = Middle value or average of two middle values in a sorted dataset
Q1 = Median of the lower half of the data
Q3 = Median of the upper half of the data
IQR = Q3 - Q1

Theorems

Quartile calculation methods
IQR as a measure of statistical dispersion

Suitable Grade Level

Grades 6-8