The Mean and Median of 7 observations are 10 and 9, respectively. If 2 is subtracted from each observation, then the new Median and the new Mean will be:

7 and 8, respectively

The correct answer is Option (2) → 7 and 8, respectively

To find the new Median and Mean, we can apply the mathematical properties of these measures of central tendency when a constant is subtracted from every observation in a dataset.

1. Effect on the Mean

The Mean ($\bar{x}$) of a set of observations is calculated as:

$\bar{x} = \frac{\sum x_i}{n}$

If a constant $k$ is subtracted from each observation ($x_i - k$), the new mean ($\bar{x}_{new}$) is:

$\bar{x}_{new} = \frac{\sum (x_i - k)}{n} = \frac{\sum x_i - nk}{n} = \bar{x} - k$

Given original Mean = $10$ and $k = 2$:

$\text{New Mean} = 10 - 2 = \mathbf{8}$

2. Effect on the Median

The Median is the middle value of a sorted data set. If every value in the set is shifted by subtracting a constant $k$, the entire distribution shifts, but the relative order remains the same. The middle value also shifts by that same constant.

$\text{New Median} = \text{Old Median} - k$

Given original Median = $9$ and $k = 2$:

$\text{New Median} = 9 - 2 = \mathbf{7}$

Conclusion

• New Median: 7
• New Mean: 8