1. 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

2. 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 \(k\)?

3. 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 \(k\)?

4. If the mean of a frequency distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\), then find the value of \(k\).

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

6. If the mean of a frequency distribution is 4.1, \(∑f_i.x_i = 132 + 5k\), and \(∑f_i = 20\), then find the value of \(k\).

7. 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.

8. 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

9. 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

10. If class width = 20, assumed mean \(A = 25\), total frequency \(y = 50\), and \(\sum f_u = -5\), then the combined mean \(\bar{x}\) will be —

(a) 25 (b) 23 (c) 24 (d) 27

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

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

13. 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 \(k\).

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