Read the given statement carefully and state T for true and F for false.
i) Mean, Median and Mode can never be same for any data.
(ii) Median of the data can less than the mean of data.
(iii) Mean of the observations is the sum of all the observations.

Options

A. `{:(i" "ii" "iii),(T" "T" "T):}`
B. `{:(i" "ii" "iii),(T" "F" "T):}`
C. `{:(i" "ii" "iii),(T" "T" "F):}`
D. `{:(i" "ii" "iii),(F" "T" "F):}`

Answer

To solve the question, we will analyze each statement one by one and determine whether they are true (T) or false (F).

### Step-by-Step Solution:

1. **Statement (i)**: "Mean, Median and Mode can never be the same for any data."
- **Analysis**: This statement is false. There are certain datasets where the mean, median, and mode can be the same. For example, in a dataset like {2, 2, 2}, the mean is 2, the median is 2, and the mode is also 2.
- **Conclusion**: F (False)

2. **Statement (ii)**: "Median of the data can be less than the mean of the data."
- **Analysis**: This statement is true. In a skewed distribution, especially a positively skewed distribution, the median can indeed be less than the mean. For example, in the dataset {1, 2, 3, 4, 100}, the mean is 22, while the median is 3.
- **Conclusion**: T (True)

3. **Statement (iii)**: "Mean of the observations is the sum of all the observations."
- **Analysis**: This statement is false. The mean is calculated by taking the sum of all observations and dividing it by the number of observations. Therefore, the statement is incorrect as it does not mention the division by the number of observations.
- **Conclusion**: F (False)

### Final Answers:
- (i) F
- (ii) T
- (iii) F

### Summary:
The answers to the statements are:
- (i) F
- (ii) T
- (iii) F