Question

A set of data with 100 observations has a mean of 267. There are six outliers in the data set, which have a mean of 688. If the six outliers are removed, what is the mean of the new data set?
A. 251.0
B. 311.6
C. 240.1
D. 284.0

Answer 1

Let

x------> the sum of a set of data with $100$ observations

Mn------> the means of the new data set

we know that

$\frac{x}{100}=267\\ \\ x=267*100\\ x=26,700$

$Mn=\frac{(x-6*688)}{(100-6) }\\ \\ Mn=\frac{(26,700-4,128)}{(94) }\\ \\ Mn=240.13$

therefore

the answer is the option C

the mean of the new data set is $240.1$

Answer 2

X*94 +688*6  = 267*100
94x+4128=26700     
94X=22572    /94
X=240.128
C is the closest answer