1. 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

2. If the assumed mean is 22, class width is 10, total frequency is 80, and the value of \(\sum{f_iu_i}\) is 16, then the actual (or true) mean will be —

(a) 23 (b) 24 (c) 25 (d) 26

3. 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 \(k\).

4. 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

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. 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 \(k\)?

7. 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

8. If \(\sum\limits_{i=1}^5 x_i = 5\) and \(\sum\limits_{i=1}^5 x_i^2 = 14\), then the value of \(\sum\limits_{i=1}^5 2x_i(x_i - 3)\) will be —

(a) 2 (b) -2 (c) 0 (d) 4

9. 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 \(k\).

10. 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 \(k\).

11. 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 \(k\).

12. 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 \(k\).

13. 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.