Find the mean deviation about the median for the following data: 4, 6, 9, 3, 10, 13, 2.

To find the mean deviation about the median for the data set 4, 6, 9, 3, 10, 13, 2, follow these steps:

Step 1: Organize the Data

First, arrange the numbers in ascending order:

• 2, 3, 4, 6, 9, 10, 13

Step 2: Calculate the Median

Since there are 7 numbers (an odd count), the median is the middle value:

• Median = 6

Step 3: Find the Absolute Deviations

Next, calculate the absolute deviations from the median:

• |2 - 6| = 4
• |3 - 6| = 3
• |4 - 6| = 2
• |6 - 6| = 0
• |9 - 6| = 3
• |10 - 6| = 4
• |13 - 6| = 7

Step 4: Calculate the Mean Deviation

Add the absolute deviations:

• Total = 4 + 3 + 2 + 0 + 3 + 4 + 7 = 23

Now, divide by the number of data points:

• Mean Deviation = Total Deviations / Number of Data Points = 23 / 7 ≈ 3.29

Final Result

The mean deviation about the median for the given data set is approximately 3.29.