Find `P_(70)` of the distribution `x_(i) : 28 , 17 , 25 , 26 , 19 , 13 , 27 , 21, 16 `

Answer

To find \( P_{70} \) of the given distribution \( x_i: 28, 17, 25, 26, 19, 13, 27, 21, 16 \), we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the data in ascending order.

**Data in ascending order:**
\[ 13, 16, 17, 19, 21, 25, 26, 27, 28 \]

### Step 2: Determine the Number of Observations
Count the total number of observations \( N \).

**Total observations \( N \):**
\[ N = 9 \]

### Step 3: Calculate the Position for \( P_{70} \)
Use the formula to find the position of \( P_{70} \):
\[ T = \frac{70}{100} \times (N + 1) \]
Substituting \( N = 9 \):
\[ T = \frac{70}{100} \times (9 + 1) = 0.7 \times 10 = 7 \]

### Step 4: Identify the 7th Observation
Since \( T = 7 \), we will look for the 7th observation in our ordered data.

**7th observation:**
The 7th observation in the ordered data is \( 26 \).

### Step 5: Calculate the Fractional Part
Since \( T \) is a whole number (7), we can directly take the 7th observation as \( P_{70} \).

### Step 6: Conclusion
Thus, \( P_{70} = 26 \).

### Summary of Steps:
1. Organize the data in ascending order.
2. Count the total number of observations.
3. Calculate the position for \( P_{70} \).
4. Identify the observation at that position.
5. If \( T \) is a whole number, \( P_{70} \) is the value at that position.