25th percentile is 20 and 75th percentile is 50, then semi interquartile range is

Options

A. 10
B. 40
C. 15
D. 25

Answer

To find the semi-interquartile range given the 25th percentile (Q1) and the 75th percentile (Q3), we can follow these steps:

### Step 1: Identify the values of Q1 and Q3
From the problem, we know:
- 25th percentile (Q1) = 20
- 75th percentile (Q3) = 50

### Step 2: Use the formula for semi-interquartile range
The semi-interquartile range (SIQR) is calculated using the formula:
\[ \text{SIQR} = \frac{Q3 - Q1}{2} \]

### Step 3: Substitute the values into the formula
Now, substituting the values of Q1 and Q3 into the formula:
\[ \text{SIQR} = \frac{50 - 20}{2} \]

### Step 4: Calculate the difference
Calculate the difference between Q3 and Q1:
\[ 50 - 20 = 30 \]

### Step 5: Divide by 2
Now, divide the result by 2 to find the semi-interquartile range:
\[ \text{SIQR} = \frac{30}{2} = 15 \]

### Conclusion
Thus, the semi-interquartile range is **15**.

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