The median of a series is 10. Two additional observations 7 and 20 are added to series. The median of new series is

Options

A. 9
B. 20
C. 7
D. 10

Answer

To find the median of the new series after adding the observations 7 and 20, we can follow these steps:

### Step 1: Understand the Original Median
The original median of the series is given as 10. This means that when the data is arranged in ascending order, the middle value (or the average of the two middle values if there is an even number of observations) is 10.

### Step 2: Add the New Observations
We are adding two new observations, 7 and 20, to the series. The new series will now include these values along with the original values.

### Step 3: Arrange the New Series
To find the new median, we need to arrange the series in ascending order. The new observations are 7 and 20. Assuming the original series has values that allow 10 to be the median, we can represent the series as follows:
- Let’s denote the original series as \( a_1, a_2, ..., a_n \) where the median is 10.
- After adding the new observations, the series becomes \( 7, a_1, a_2, ..., a_n, 10, a_{n+1}, a_{n+2}, 20 \).

### Step 4: Determine the New Median
Since we have added two observations, the total number of observations in the new series becomes \( n + 2 \).

1. If \( n \) is odd, then \( n + 2 \) will be odd, and the median will be the middle value.
2. If \( n \) is even, then \( n + 2 \) will be even, and the median will be the average of the two middle values.

In both cases, since the original median is 10, and the new observations (7 and 20) do not change the position of 10 in the ordered series, the median remains 10.

### Final Answer
Thus, the median of the new series after adding the observations 7 and 20 is **10**.

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