If semi Inter quartile range is `19.38,Q_(3)=72.5` then , `Q_(1)` is

Options

A. (a)`38.75`
B. (b)`35.75`
C. (c)`33.74`
D. (d)`34.75`

Answer

To find \( Q_1 \) given the semi-interquartile range and \( Q_3 \), we can follow these steps:

### Step 1: Understand the formula for semi-interquartile range
The semi-interquartile range (denoted as \( Q_d \)) is calculated using the formula:
\[ Q_d = \frac{Q_3 - Q_1}{2} \]

### Step 2: Substitute the known values into the formula
We know from the problem that:
- \( Q_d = 19.38 \)
- \( Q_3 = 72.5 \)

Substituting these values into the formula gives:
\[ 19.38 = \frac{72.5 - Q_1}{2} \]

### Step 3: Eliminate the fraction by multiplying both sides by 2
To eliminate the fraction, multiply both sides of the equation by 2:
\[ 2 \times 19.38 = 72.5 - Q_1 \]
This simplifies to:
\[ 38.76 = 72.5 - Q_1 \]

### Step 4: Rearrange the equation to solve for \( Q_1 \)
Now, rearranging the equation to isolate \( Q_1 \):
\[ Q_1 = 72.5 - 38.76 \]

### Step 5: Perform the subtraction
Calculating the right side gives:
\[ Q_1 = 33.74 \]

### Final Answer
Thus, the value of \( Q_1 \) is:
\[ \boxed{33.74} \]

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