1. 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

2. 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 \(\bar{x}\)?

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

4. If \(u_i = \frac{x_i - 30}{10}\), \(∑f_i = 50\), and \(∑u_i f_i = 25\), then what is the value of \(\bar{x}\)?

5. If \(u_i = \frac{x_i − 35}{10}\), \(Σf_iu_i = 30\), and \(Σf_i = 60\), then find the value of \(\bar{x}\).

6. If \(u_i = \cfrac{x_i - 35}{10}\), \(∑f_i u_i = 30\), and \(∑f_i = 60\), then the value of \(\bar{x}\) is –

(a) 40 (b) 20 (c) 80 (d) None of these

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. Given: \[ u_i = \frac{x_i - 25}{10}, \quad \sum f_i u_i = 20, \quad \sum f_i = 100 \] Find the value of \(\bar{x}\) (the mean).

9. If \(u_i=\cfrac{x_i−35}{10} , Σf_iu_i=30\), and \(Σf_i=60\), then determine the value of \(\bar{x}\).

10. If \(u_i=\cfrac{x_i-35}{10}\), \(∑f_i u_i=30\), and \(∑f_i=60\), then determine the value of \(\bar{x}\).

11. If \(u_i=\cfrac{x_i−35}{10} , Σf_iu_i=30\) and \(Σf_i=30\), find the value of \(\bar{x}\).

12. If \(u_i = \cfrac{x_i − 35}{10}\), \(Σf_i u_i = 30\), and \(Σf_i = 60\), then find the value of \(\bar{x}\).

13. If \(∑f_i(x_i - a) = 400\), \(∑f_i = 50\), and \(a\) (assumed mean) = 52, then the value of the combined mean \(\bar{x}\) is –

(a) 52 (b) 60 (c) 80 (d) 90

14. 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

15. If \( u_i = \frac{x_i - 45}{10} \), \( ∑f_i u_i = -16 \), and \( ∑f_i = 200 \), then what is the value of \( \bar{x} \)?

16. 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 \(k\).

17. 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 \(k\).

18. In a statistical distribution, the average (mean) is 7 and \(\sum f_i x_i = 140\). Find the value of \(\sum f_i\).