The median and S.D. of a distribution are 20 and 4 respetively. If eahc item is increased by 2, the new median and S.D. are

Options

A. 20, 6
B. 22, 6
C. 18, 6
D. 22, 4

Answer

To solve the problem, we need to determine the new median and standard deviation after each item in the distribution is increased by 2.

### Step-by-Step Solution:

1. **Understanding the Given Values**:
- The original median of the distribution is given as 20.
- The original standard deviation (S.D.) of the distribution is given as 4.

2. **Effect on Median**:
- When each item in a distribution is increased by a constant (in this case, 2), the median also increases by that same constant.
- Therefore, the new median can be calculated as:
\[ \text{New Median} = \text{Original Median} + 2 = 20 + 2 = 22 \]

3. **Effect on Standard Deviation**:
- The standard deviation measures the spread of the data around the mean. It is not affected by adding or subtracting a constant from each data point.
- Thus, the new standard deviation remains the same as the original standard deviation:
\[ \text{New S.D.} = \text{Original S.D.} = 4 \]

4. **Final Results**:
- The new median is 22.
- The new standard deviation is 4.

### Conclusion:
The new median and standard deviation after increasing each item by 2 are:
- **New Median**: 22
- **New Standard Deviation**: 4