1. 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
2. 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
3. If \(u_i = \frac{x_i - 30}{10}\), \(∑f_i = 50\), and \(∑u_i f_i = 25\), then what is the value of \(\bar{x}\)?
4. 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 \(k\)?
5. 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
6. If \(\sum_{i=1}^n (x_i - 3) = 0\) and \(\sum_{i=1}^n (x_i + 3) = 66\), then find the values of \(\bar{x}\) (the mean) and \(n\).
7. If for a set of data, \[ \sum_{i=1}^n (x_i - 7) = -8 \quad \text{and} \quad \sum_{i=1}^n (x_i + 3) = 72, \] then find the values of \(\bar{x}\) (the mean) and \(n\) (the number of data points).
8. 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 \(k\)?
9. If \(x^2 - px + 12 = (x - 3)(x - a)\) is an identity, then the values of \(a\) and \(p\) respectively are?
(a) \(a = 4, p = 7\) (b) \(a = 7, p = 4\) (c) \(a = 4, p =-7\) (d) \(a =-4, p = 7\)
10. 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).
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. 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 \(k\).
14. 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.
