1. **Stating the problem:** We are asked to find the 4th quartile (Desil ke-4 or D4) of the given data set: 70, 85, 90, 75, 80, 95, 85, 70, 80, 90.
2. **Understanding the concept:** The 4th decile (D4) divides the data into 10 equal parts, so D4 corresponds to the 40th percentile.
3. **Step 1: Sort the data in ascending order:**
$$70, 70, 75, 80, 80, 85, 85, 90, 90, 95$$
4. **Step 2: Calculate the position of D4 using the formula:**
$$\text{Position of } D4 = \frac{4}{10} \times (n + 1)$$
where $n$ is the number of data points.
5. **Step 3: Substitute $n=10$:**
$$\text{Position of } D4 = \frac{4}{10} \times (10 + 1) = 0.4 \times 11 = 4.4$$
6. **Step 4: Interpret the position:**
The 4.4th value means we take the 4th value plus 0.4 times the difference between the 5th and 4th values.
7. **Step 5: Identify the 4th and 5th values:**
4th value = 80
5th value = 80
8. **Step 6: Calculate D4:**
$$D4 = 80 + 0.4 \times (80 - 80) = 80 + 0 = 80$$
**Final answer:** The 4th decile (D4) of the data is **80**.
Decile Fourth Fb6413
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