The marks of 9 students in a test were 13,17,20,3,5,3,20,15 and 18. Find quartile deviation.

Answer

To find the quartile deviation of the given marks of 9 students, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the given marks in ascending order. The marks are:
- 13, 17, 20, 3, 5, 3, 20, 15, 18

Arranging these marks in ascending order gives us:
- 3, 3, 5, 13, 15, 17, 18, 20, 20

### Step 2: Find the Median (Q2)
The median (Q2) is the middle value of the ordered data. Since there are 9 observations (an odd number), the median is the value at position (n + 1) / 2, where n is the number of observations.

- Position of median = (9 + 1) / 2 = 10 / 2 = 5

The 5th value in the ordered list is 15. Thus, Q2 = 15.

### Step 3: Find Q1 (First Quartile)
Q1 is the median of the lower half of the data. The lower half consists of the first four numbers:
- 3, 3, 5, 13

To find Q1, we take the average of the two middle values (2nd and 3rd values):
- Q1 = (3 + 5) / 2 = 8 / 2 = 4

### Step 4: Find Q3 (Third Quartile)
Q3 is the median of the upper half of the data. The upper half consists of the last four numbers:
- 17, 18, 20, 20

To find Q3, we take the average of the two middle values (2nd and 3rd values):
- Q3 = (18 + 20) / 2 = 38 / 2 = 19

### Step 5: Calculate the Quartile Deviation (QD)
The formula for quartile deviation is:
\[ QD = \frac{Q3 - Q1}{2} \]

Substituting the values we found:
\[ QD = \frac{19 - 4}{2} = \frac{15}{2} = 7.5 \]

### Final Answer
The quartile deviation of the marks is **7.5**.

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