The median of the following data : 0, 2, 2, 2, -3, 5, - 1, 5, 5, -3, 6, 6, 5, 6 is n x 0.7. Find the value of n.

Answer

To find the value of \( n \) such that the median of the given data is \( n \times 0.7 \), we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the given data set in ascending order. The data provided is:
\[ 0, 2, 2, 2, -3, 5, -1, 5, 5, -3, 6, 6, 5, 6 \]

Arranging these numbers in ascending order, we get:
\[ -3, -3, -1, 0, 2, 2, 2, 5, 5, 5, 5, 6, 6, 6 \]

### Step 2: Count the Number of Observations
Next, we count the total number of observations in the data set. There are 14 numbers in total.

### Step 3: Determine the Median Position
Since there are 14 observations (an even number), the median is calculated as the average of the two middle numbers. The positions of these middle numbers can be found using the formula:
- For an even number of observations, the median is the average of the \( \frac{n}{2} \)th and \( \left(\frac{n}{2} + 1\right) \)th observations.

Here, \( n = 14 \):
- The \( \frac{14}{2} = 7 \)th observation
- The \( \left(\frac{14}{2} + 1\right) = 8 \)th observation

### Step 4: Find the 7th and 8th Observations
From our ordered data:
- The 7th observation is \( 2 \)
- The 8th observation is \( 5 \)

### Step 5: Calculate the Median
Now, we calculate the median:
\[ \text{Median} = \frac{\text{7th observation} + \text{8th observation}}{2} = \frac{2 + 5}{2} = \frac{7}{2} = 3.5 \]

### Step 6: Set Up the Equation
According to the problem, the median can also be expressed as:
\[ \text{Median} = n \times 0.7 \]
Thus, we have:
\[ 3.5 = n \times 0.7 \]

### Step 7: Solve for \( n \)
To find \( n \), we can rearrange the equation:
\[ n = \frac{3.5}{0.7} \]
Calculating this gives:
\[ n = 5 \]

### Final Answer
The value of \( n \) is \( 5 \).

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