1. For a frequency distribution, the mean is given as 8.1; \(\sum f_i x_i = 132+5k\) and \(\sum f_i = 20\). Find the value of \(k\).

2. If \(\sum{f_ix_i} = 216\), \(\sum{f_i} = 16\), and the combined mean is \(13.5 + p\), then what is the value of \(p\)?

(a) 0 (b) 1 (c) 0.1 (d) 0.01

3. If \(u_i = \cfrac{x_i - 25}{10}\), \(\sum f_i u_i = 20\), and \(\sum f_i = 100\), then what is the value of \(\bar{x}\)?

4. If the mean of a frequency distribution is 8.1, \(\sum f_i x_i = 132 + 5k\) and \(\sum f_i = 20\), then find the value of \(k\).

5. **"In a statistical distribution, if the mean is 8.1, \(\sum f_i x_i = 132 + 5k\), and \(\sum f_i = 20\), then \(k =\) _____"**

6. In a statistical distribution, the mean is 8.1, \( \sum f_i x_i = 132 + k \), and \( \sum f_i = 20 \). Find the value of \( k \).

7. If \(\sum f_iu_i = 10\), class width = 20, \(\sum f_i = 40 + k\), the combined mean is 54, and the assumed mean is 50, then what is the value of \(k\)?

8. If \(u_i = \cfrac{x_i - 20}{10}\), \(\sum{f_iu_i} = 15\), and \(\sum{f_i} = 80\), then what will be the value of \(\bar{x}\)?

(a) 21.875 (b) 20.875 (c) 21.800 (d) 20.125

9. If \(\sum \limits_{i=1}^n (x_i - 7) = -8\) and \(\sum \limits_{i=1}^n (x_i + 3) = 72\), then what are the values of \(\bar{x}\) (the mean of \(x_i\)) and \(n\) (the number of terms)?

(a) \(\bar{x}=5, n=8\) (b) \(\bar{x}=6, n=8\) (c) \(\bar{x}=4, n=7\) (d) \(\bar{x}=8, n=6\)

10. Given: \(u_i = \frac{x_i - 20}{10}\), \(\sum f_i u_i = 50\), \(\sum f_i = 100\) Find the value of \(\bar{x}\) (mean).

11. If the mean of a statistical distribution is 4.1, \(∑f_i x_i = 132 + 5k\), and \(∑f_i = 20\), then what is the value of \(k\)?

12. If \(\sum(x_i - 3) = 0\) and \(\sum(x_i + 3) = 66\), then find the values of \(\bar{x}\) (mean) and \(n\) (number of observations).

13. The mean of a statistical distribution is \( 4.1 \), given \( ∑f_i.x_i = 132 + 5k \) and \( ∑f_i = 20 \). Find the value of \( k \).

14. If the mean of a statistical distribution is **4.1**, \(∑f_i.x_i = 132+5k\), and \(∑f_i=20\), determine the value of \(k\).

15. The mean of a statistical distribution is 4.1. Given that \(∑f_i.x_i = 132 + 5k\) and \(∑f_i = 20\), find the value of \(k\).

16. The mean of a statistical distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\). Find the value of \(k\).

17. Here’s the English translation: *If the mean of a statistical distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\), then what is the value of \(k\)?* Would you like help solving it too? I’d be glad to walk through it with you.

18. If \(u_i =\cfrac{x_i - 25}{10}\), \(\sum f_i u_i = 20\), and \(\sum f_i = 100\), then find the value of \(\bar{x}\).