The semi-inter quartile range of the observations 9, 12, 14, 6, 23, 36, 20, 7, 42 and 32 is

Options

A. 12.75
B. 12.5
C. 11.5
D. 9.5

Explanation

To find the semi-interquartile range (also known as the quartile deviation) of the given observations, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the given observations in ascending order.

**Given Observations:** 9, 12, 14, 6, 23, 36, 20, 7, 42, 32

**Arranged in Ascending Order:** 6, 7, 9, 12, 14, 20, 23, 32, 36, 42

### Step 2: Find the Quartiles
To find the semi-interquartile range, we need to calculate the first quartile (Q1) and the third quartile (Q3).

**Total number of observations (n) = 10**

**Q1 Calculation:**
- The first quartile (Q1) is the median of the first half of the data.
- The first half of the data (first 5 observations): 6, 7, 9, 12, 14
- The median of these 5 numbers is the third number (since there are 5 numbers): **Q1 = 9**

**Q3 Calculation:**
- The third quartile (Q3) is the median of the second half of the data.
- The second half of the data (last 5 observations): 20, 23, 32, 36, 42
- The median of these 5 numbers is the third number: **Q3 = 32**

### Step 3: Calculate the Semi-Interquartile Range
Now, we can use the formula for the semi-interquartile range:

\[ \text{Semi-Interquartile Range} = \frac{Q3 - Q1}{2} \]

Substituting the values we found:

\[ \text{Semi-Interquartile Range} = \frac{32 - 9}{2} = \frac{23}{2} = 11.5 \]

### Final Answer
The semi-interquartile range of the observations is **11.5**.

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