## 1. The mean of the first n natural numbers is:

### Answer:

### Explanation:

The sum of the first n natural numbers is n(n+1)/2. So, the mean = [n(n+1)/2] / n = (n+1)/2.

## 2. The median of the data: 6, 8, 9, 12, 15 is:

### Answer:

### Explanation:

When data is arranged in ascending or descending order, the median is the middle number.

## 3. The mode of the data: 5, 5, 6, 6, 6, 7, 7 is:

### Answer:

### Explanation:

The mode is the number that appears most frequently. Here, 6 appears three times, which is the highest frequency.

## 4. The range of the data: 2, 5, 8, 12, 15 is:

### Answer:

### Explanation:

Range = Highest value – Lowest value = 15 – 2 = 13.

## 5. The mean of the data: 4, 5, 6, 7, 8 is:

### Answer:

### Explanation:

Mean = (4+5+6+7+8)/5 = 30/5 = 6.

## 6. For grouped data, the formula to find the mean is:

### Answer:

### Explanation:

For grouped data, the mean is found using the formula: Mean = Σfi.xi / Σfi, where fi is the frequency and xi is the class mark.

## 7. The mode for the data which doesn't have any number repeating more than once is called:

### Answer:

### Explanation:

If no number repeats more than once, the data set doesn't have a mode.

## 8. The value of median in the data set: 2, 4, 6, 8, 10, 12, 14 is:

### Answer:

### Explanation:

In an odd number of ordered data, the median is the middle number.

## 9. The value below which 50% of data falls is called:

### Answer:

### Explanation:

By definition, the median divides data into two equal parts.

## 10. The sum of the deviation of all observations from their mean is:

### Answer:

### Explanation:

The sum of the deviation of all the observations from their mean is always zero because of the properties of mean.