If upper quartile and inter-quartile range of a data are 55 and 5 respectively, then find the value of lower quartile

Answer

To find the value of the lower quartile (QL) given the upper quartile (QU) and the inter-quartile range (IQR), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Upper Quartile (QU) = 55
- Inter-Quartile Range (IQR) = 5

2. **Understand the Formula for Inter-Quartile Range:**
The inter-quartile range is defined as:
\[ IQR = QU - QL \]
Rearranging this gives us:
\[ QL = QU - IQR \]

3. **Substitute the Known Values into the Formula:**
Now, substitute the values of QU and IQR into the rearranged formula:
\[ QL = 55 - 5 \]

4. **Calculate the Value of QL:**
Perform the subtraction:
\[ QL = 50 \]

5. **Final Answer:**
The value of the lower quartile (QL) is 50.

### Summary of Steps:
1. Identify the upper quartile and inter-quartile range.
2. Use the formula \( IQR = QU - QL \) to express QL in terms of QU and IQR.
3. Substitute the known values into the equation.
4. Perform the calculation to find QL.