Statistics And Probability Question 371
Question: The first of two samples has 100 items with mean 15 and SD 3. If the whole group has 250 items with mean 15.6 and $ SD=\sqrt{13.44} $ the SD of the second group is
Options:
A) 5
B) 4
C) 6
D) 3.52
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Use $ {{\sigma }^{2}}=\frac{n_1(\sigma _1^{2}+d_1^{2})+n_2(\sigma _2^{2}+d_2^{2})}{n_1+n_2} $ where $ d_1=m_1-a,d_2=m_2-a,a $ being the mean of the whole group. Let $ m_2= $ mean of the second group
$ \therefore 15.6=\frac{100\times 15+150\times m_2}{250}\Rightarrow m_2=16 $ Thus, $ (100\times 9+150\times {{\sigma }^{2}}) $ $ 13.44=\frac{+100\times {{(0.6)}^{2}}+150\times {{(0.4)}^{2}}}{250} $
$ \Rightarrow \sigma =4 $
BETA
