Discussion
The first group sample has 100 items with mean 15 and standard deviation 3.0. If the whole group has 250 items with mean 15.6 and standard deviation \(\sqrt{13.44}\). What is the standard deviation of the second group ?
Answer: B
The standard deviation of the second group is 4.
The second group has 250 - 100 = 150 items. Its mean, from the combined total:
\[ \begin{aligned} \bar{x}_{2} &= \frac{250(15.6) - 100(15)}{150} \\ &= \frac{2400}{150} = 16 \end{aligned} \]
So \(d_{1} = 15 - 15.6 = -0.6\) and \(d_{2} = 16 - 15.6 = 0.4\). The combined variance is 13.44, since the combined SD is \(\sqrt{13.44}\):
\[ \begin{aligned} 250(13.44) &= 100(9 + 0.36) \\ &\quad + 150(\sigma_{2}^{2} + 0.16) \\ 3360 &= 936 + 24 + 150\sigma_{2}^{2} \\ \sigma_{2}^{2} &= 16,\quad \sigma_{2} = 4 \end{aligned} \]
Check the others: with a second-group SD of 2, 6 or 8 the combined variance would come out as 6.24, 25.44 or 42.24 instead of 13.44.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development