Statistics And Probability Question 387
Question: The mean and SD of 63 children on an arithmetic test are respectively 27, 6 and 7.1. to them are added a new group of 26 who had less training and whose mean is 19.2 and SD. 6.2 The values of the combined group differ from the original as to (i) the mean and (ii) the SD is
Options:
A) 25.1, 7.8
B) 2.3, 0.8
C) 1.5, 0.9
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Mean and SD $ \sigma $ of the combined group are $ m=\frac{63\times 27.6+26\times 19.2}{63+26}=25.1 $ Thus, AM is decreased by $ 27.6-25.1=2.5. $ $ {{\sigma }^{2}}=\frac{63\times {{(7.1)}^{2}}+26\times {{(6.2)}^{2}}}{89} $ $ +\frac{63{{(25.1-27.6)}^{2}}+26{{(25.1-19.2)}^{2}}}{89} $
$ \Rightarrow \sigma =7.8 $ (approx.)
BETA
