From the following data: find
(i) Median (ii) Upper quartile (iii) Inter quartile range:
25, 10,40,88,45,60,77,36,18,95,56,65,7,0,38 and 83

Answer

To solve the problem, we will follow these steps:

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

Given data:
25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38, 83

Arranging in ascending order:
0, 7, 10, 18, 25, 36, 38, 40, 45, 56, 60, 65, 77, 83, 88, 95

### Step 2: Find the Median
To find the median, we need to determine the middle value of the ordered data. Since there are 16 numbers (even), the median will be the average of the 8th and 9th values.

The 8th value is 40 and the 9th value is 45.

Calculating the median:
\[ \text{Median} = \frac{40 + 45}{2} = \frac{85}{2} = 42.5 \]

### Step 3: Find the Upper Quartile (Q3)
The upper quartile (Q3) is the value at the 75th percentile. To find this, we use the formula:
\[ Q3 = \frac{3n}{4} \]
where \( n \) is the number of data points.

Substituting \( n = 16 \):
\[ Q3 = \frac{3 \times 16}{4} = 12 \]
The 12th value in the ordered data is 65.

### Step 4: Find the Lower Quartile (Q1)
The lower quartile (Q1) is the value at the 25th percentile. To find this, we use the formula:
\[ Q1 = \frac{n}{4} \]

Substituting \( n = 16 \):
\[ Q1 = \frac{16}{4} = 4 \]
The 4th value in the ordered data is 18.

### Step 5: Calculate the Interquartile Range (IQR)
The interquartile range is calculated as:
\[ IQR = Q3 - Q1 \]
Substituting the values we found:
\[ IQR = 65 - 18 = 47 \]

### Final Results
- Median: 42.5
- Upper Quartile (Q3): 65
- Interquartile Range (IQR): 47

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