the mean deviation from the median of discrete data 3,9,4,6,4,7,12,19,8 is

To find the mean deviation from the median for the given discrete data set \(3, 9, 4, 6, 4, 7, 12, 19, 8\), we can follow these steps:

1. **Arrange the data in ascending order:**
   \(3, 4, 4, 6, 7, 8, 9, 12, 19\)

2. **Find the median:**
   Since there are 9 data points (an odd number), the median is the middle value, which is the 5th value in the ordered list.
   \[
   \text{Median} = 7
   \]

3. **Calculate the absolute deviations from the median:**
   \[
   |3 - 7| = 4
   \]
   \[
   |4 - 7| = 3
   \]
   \[
   |4 - 7| = 3
   \]
   \[
   |6 - 7| = 1
   \]
   \[
   |7 - 7| = 0
   \]
   \[
   |8 - 7| = 1
   \]
   \[
   |9 - 7| = 2
   \]
   \[
   |12 - 7| = 5
   \]
   \[
   |19 - 7| = 12
   \]

4. **Sum the absolute deviations:**
   \[
   4 + 3 + 3 + 1 + 0 + 1 + 2 + 5 + 12 = 31
   \]

5. **Calculate the mean deviation from the median:**
   \[
   \text{Mean Deviation} = \frac{\text{Sum of Absolute Deviations}}{\text{Number of Data Points}} = \frac{31}{9} \approx 3.44
   \]

The mean deviation from the median is approximately \(3.44\).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How is the mean deviation from the mean calculated?
2. What is the median of a data set with an even number of observations?
3. How does the presence of outliers affect the mean deviation?
4. What are the advantages of using the median over the mean in skewed distributions?
5. How do you calculate the range of a data set?
6. What is the interquartile range (IQR) and how is it calculated?
7. How does the mean absolute deviation differ from the standard deviation?
8. Why is the mean deviation always non-negative?

**Tip:** The mean deviation is useful for understanding the spread of data points around the median, especially in skewed distributions where the mean can be misleading.

Learn how to calculate the mean deviation from the median for a set of discrete data (3, 9, 4, 6, 4, 7, 12, 19, 8) with a step-by-step explanation. This problem covers statistical concepts including mean deviation and median calculations. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation