Find the mean deviation from the median for the following data :
38,70,48,34,63,42,55,44,53,47

Answer

To find the mean deviation from the median for the given data set, we will follow these steps:

### Step 1: Arrange the data in ascending order
The given data is: 38, 70, 48, 34, 63, 42, 55, 44, 53, 47.

**Arranging in ascending order:**
34, 38, 42, 44, 47, 48, 53, 55, 63, 70.

### Step 2: Calculate the median
Since there are 10 observations (an even number), the median is the average of the 5th and 6th terms.

**Finding the 5th and 6th terms:**
- 5th term = 47
- 6th term = 48

**Calculating the median:**
Median = (47 + 48) / 2 = 95 / 2 = 47.5.

### Step 3: Calculate the absolute deviations from the median
Now we will find the absolute deviations of each observation from the median (47.5).

**Calculating absolute deviations:**
- |34 - 47.5| = 13.5
- |38 - 47.5| = 9.5
- |42 - 47.5| = 5.5
- |44 - 47.5| = 3.5
- |47 - 47.5| = 0.5
- |48 - 47.5| = 0.5
- |53 - 47.5| = 5.5
- |55 - 47.5| = 7.5
- |63 - 47.5| = 15.5
- |70 - 47.5| = 22.5

### Step 4: Sum of absolute deviations
Now, we will sum all the absolute deviations calculated in the previous step.

**Summing the absolute deviations:**
13.5 + 9.5 + 5.5 + 3.5 + 0.5 + 0.5 + 5.5 + 7.5 + 15.5 + 22.5 = 84.

### Step 5: Calculate the mean deviation
The mean deviation is calculated by dividing the sum of absolute deviations by the number of observations.

**Calculating mean deviation:**
Mean Deviation = Total Absolute Deviations / Number of Observations = 84 / 10 = 8.4.

### Final Answer:
The mean deviation from the median for the given data is **8.4**.

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