1. 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

2. 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 \(k\)?

3. 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.

4. 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

5. If \(∑f_i d_i = 400\), \(∑f_i = 50\), and \(a =\) assumed mean \(= 52\), then the value of the combined mean is –

(a) 52 (b) 60 (c) 80 (d) 55

6. 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

7. 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 \(k\).

8. 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 \(k\).

9. 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 \(k\).

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

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

14. 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

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

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. 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 \(\bar{x}\)?

18. If the mean of the frequency distribution is 62.8 and the total frequency is 50, then what are the values of \(x\) and \(y\) given the following table: | Class | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | 100–120 | |-------------|------|--------|--------|--------|---------|----------| | Frequency | 5 | \(x+y\) | 10 | \(y−x\) | 7 | 8 |