Two data sets S and R are defined as follows :
Data set S : 28, 30, 25, 28, 27
Data set R : 22, 19, 15, 17, 21, 25
By how much is the median of data set S greater than the median of data set R ?

Options

A. 5
B. 6
C. 7
D. 8

Answer

To find out by how much the median of data set S is greater than the median of data set R, we will follow these steps:

### Step 1: Find the median of data set S.
Data set S: 28, 30, 25, 28, 27

1. **Arrange the data in ascending order**:
- The arranged data set S is: 25, 27, 28, 28, 30.

2. **Count the number of elements**:
- There are 5 elements in data set S (which is odd).

3. **Calculate the median**:
- The median is given by the formula:
\[ \text{Median} = \frac{N + 1}{2} \]
- Here, \(N = 5\), so:
\[ \text{Median} = \frac{5 + 1}{2} = 3 \]
- The 3rd element in the ordered list is 28.
- Thus, the median of data set S is **28**.

### Step 2: Find the median of data set R.
Data set R: 22, 19, 15, 17, 21, 25

1. **Arrange the data in ascending order**:
- The arranged data set R is: 15, 17, 19, 21, 22, 25.

2. **Count the number of elements**:
- There are 6 elements in data set R (which is even).

3. **Calculate the median**:
- The median for an even number of elements is calculated as:
\[ \text{Median} = \frac{X_{N/2} + X_{(N/2) + 1}}{2} \]
- Here, \(N = 6\), so:
- The 3rd element is 19 and the 4th element is 21.
\[ \text{Median} = \frac{19 + 21}{2} = \frac{40}{2} = 20 \]
- Thus, the median of data set R is **20**.

### Step 3: Find the difference between the medians.
- Now we need to find how much the median of data set S is greater than the median of data set R:
\[ \text{Difference} = \text{Median of S} - \text{Median of R} = 28 - 20 = 8 \]

### Final Answer:
The median of data set S is greater than the median of data set R by **8**.

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