To solve the question, we need to evaluate each statement one by one and determine whether they are true (T) or false (F).
### Statement (i):
**If the mean height of 8 students is 152 cm and two more students of height 143 cm and 156 cm join the group, then the new mean height is 151.5 cm.**
1. **Calculate the total height of the first 8 students:**
\[
\text{Total height} = \text{Mean height} \times \text{Number of students} = 152 \, \text{cm} \times 8 = 1216 \, \text{cm}
\]
2. **Add the heights of the two new students:**
\[
\text{New total height} = 1216 \, \text{cm} + 143 \, \text{cm} + 156 \, \text{cm} = 1216 + 299 = 1515 \, \text{cm}
\]
3. **Calculate the new mean height:**
\[
\text{New mean height} = \frac{\text{New total height}}{\text{Total number of students}} = \frac{1515 \, \text{cm}}{10} = 151.5 \, \text{cm}
\]
**Conclusion for Statement (i): True (T)**
---
### Statement (ii):
**The sum of the maximum and minimum values of a variable is called its range.**
1. **Understand the definition of range:**
- The range of a set of data is defined as the difference between the maximum and minimum values, not the sum.
- Therefore, the correct formula for range is:
\[
\text{Range} = \text{Maximum value} - \text{Minimum value}
\]
**Conclusion for Statement (ii): False (F)**
---
### Statement (iii):
**For the given data 15, 11, 17, 15, 18, 19, 21, 15, 18, 21, 17, 15, the mode is 15.**
1. **Count the frequency of each number:**
- 15 appears 4 times.
- 11 appears 1 time.
- 17 appears 2 times.
- 18 appears 2 times.
- 19 appears 1 time.
- 21 appears 2 times.
2. **Identify the mode:**
- The mode is the number that appears most frequently. Here, 15 appears the most (4 times).
**Conclusion for Statement (iii): True (T)**
---
### Final Answers:
- (i) T
- (ii) F
- (iii) T
