Runs scored by a batsman in 10 innings are : 38, 70,48,34,42,55,63,46,54,44
The mean deviation is

Options

A. 8.6
B. 6.4
C. 10.6
D. 9.6

Explanation

To find the mean deviation of the runs scored by a batsman in 10 innings, we will follow these steps:

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

Arranging these values in ascending order gives us:
34, 38, 42, 44, 46, 48, 54, 55, 63, 70.

### Step 2: Calculate the median
Since we have 10 data points (even number), the median will be the average of the 5th and 6th values in the ordered list.

The 5th value is 46 and the 6th value is 48.

Median (M) = (46 + 48) / 2 = 94 / 2 = 47.

### Step 3: Calculate the absolute deviations from the median
Now, we will calculate 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 will sum all the absolute deviations calculated in the previous step:

Sum = 13 + 9 + 5 + 3 + 1 + 1 + 7 + 8 + 16 + 23 = 86.

### Step 5: Calculate the mean deviation
Finally, we calculate the mean deviation by dividing the sum of absolute deviations by the total number of observations (N = 10):

Mean Deviation = Sum of absolute deviations / N = 86 / 10 = 8.6.

### Final Answer
The mean deviation of the runs scored by the batsman is **8.6**.

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