If the quartile deviation is 1.79 and the first quartile is 5.86. Find the third quartile.

Options

A. 9.44
B. 7.46
C. 6
D. 4.99

Answer

To find the third quartile (Q3) given the quartile deviation (QD) and the first quartile (Q1), we can follow these steps:

### Step 1: Understand the Quartile Deviation Formula
The quartile deviation (QD) is defined as:
\[ QD = \frac{Q3 - Q1}{2} \]
Where:
- \( Q3 \) is the third quartile
- \( Q1 \) is the first quartile

### Step 2: Rearrange the Formula to Find Q3
From the formula, we can rearrange it to solve for \( Q3 \):
\[ Q3 = Q1 + 2 \times QD \]

### Step 3: Substitute the Given Values
We are given:
- \( Q1 = 5.86 \)
- \( QD = 1.79 \)

Now, substitute these values into the rearranged formula:
\[ Q3 = 5.86 + 2 \times 1.79 \]

### Step 4: Calculate the Value of Q3
First, calculate \( 2 \times 1.79 \):
\[ 2 \times 1.79 = 3.58 \]

Now, add this to \( Q1 \):
\[ Q3 = 5.86 + 3.58 = 9.44 \]

### Final Answer
Thus, the value of the third quartile \( Q3 \) is:
\[ \boxed{9.44} \]

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