The scores of a batsman in ten innings are : 55,34,48,38,70,44,54,46,63,42 Find the mean deviation about the median.

Answer

To find the mean deviation about the median for the given scores of a batsman in ten innings, we will follow these steps:

### Step 1: Arrange the scores in ascending order
The scores given are: 55, 34, 48, 38, 70, 44, 54, 46, 63, 42.

Arranging them in ascending order:
34, 38, 42, 44, 46, 48, 54, 55, 63, 70.

### Step 2: Find the median
Since we have 10 observations (an even number), the median is calculated as the average of the 5th and 6th terms.

- 5th term = 46
- 6th term = 48

Calculating the median:
\[ \text{Median} = \frac{46 + 48}{2} = \frac{94}{2} = 47 \]

### Step 3: Calculate the absolute deviations from the median
Now, we will find the absolute deviations of each score from the median (47).

- |34 - 47| = 13
- |38 - 47| = 9
- |42 - 47| = 5
- |44 - 47| = 3
- |46 - 47| = 1
- |48 - 47| = 1
- |54 - 47| = 7
- |55 - 47| = 8
- |63 - 47| = 16
- |70 - 47| = 23

### Step 4: Sum the absolute deviations
Now, we sum all the absolute deviations:
\[ 13 + 9 + 5 + 3 + 1 + 1 + 7 + 8 + 16 + 23 = 86 \]

### Step 5: Calculate the mean deviation
Finally, we divide the total absolute deviation by the number of observations (n = 10):
\[ \text{Mean Deviation} = \frac{86}{10} = 8.6 \]

### Final Answer
The mean deviation about the median is **8.6**.

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