Calculate sixty first percentile from the following data of the marks obtained by 10 students is an examination : 22,26,14,30,18,11,35,41,12,32

Answer

To calculate the 61st percentile from the given data of marks obtained by 10 students, follow these steps:

### Step 1: Write down the data
The marks obtained by the 10 students are:
22, 26, 14, 30, 18, 11, 35, 41, 12, 32.

### Step 2: Arrange the data in ascending order
To find the percentile, we first need to arrange the data in ascending order:
11, 12, 14, 18, 22, 26, 30, 32, 35, 41.

### Step 3: Determine the total number of observations (N)
Count the number of observations in the data set:
N = 10 (since there are 10 students).

### Step 4: Calculate the rank (position) of the 61st percentile
Use the formula for the rank (position) of the percentile:
\[ P = \frac{61 \times (N + 1)}{100} \]
Substituting the values:
\[ P = \frac{61 \times (10 + 1)}{100} = \frac{61 \times 11}{100} = \frac{671}{100} = 6.71 \]

### Step 5: Identify the terms corresponding to the rank
Since P = 6.71, we need to find the 6th and 7th terms in the ordered data:
- 6th term = 26
- 7th term = 30

### Step 6: Calculate the 61st percentile using interpolation
To find the 61st percentile, we use the formula:
\[ \text{Percentile} = \text{6th term} + (0.71 \times (\text{7th term} - \text{6th term})) \]
Substituting the values:
\[ \text{Percentile} = 26 + (0.71 \times (30 - 26)) \]
\[ = 26 + (0.71 \times 4) \]
\[ = 26 + 2.84 \]
\[ = 28.84 \]

### Conclusion
Hence, the 61st percentile of the marks obtained by the students is **28.84**.

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