Question

Given a data set, which of the following is most likely to be the percentage of

data within four standard deviations of the mean?

94%

75%

95%

89%

2)

If the mean of a data set is 5 and the data is said to be symmetric,

then the median will be

3

5

1

7

Answer 1

1st part:

chebychev's inequality states that,

Let X be a random variable with finite expected value and non-zero variance .Then for any real no. k>0

P(|X- |)  

in the given problem we have to find P(|X- |)  

from chebychev's inequality, we can write

P(|X- |)  

putting k=4,P(|X- |)  

hence 94% is most likely to be the percentage of data within four standard deviation of mean

2nd part:

for symmetric distribution mean=median=mode

as the mean of the data=5

so the median of the data=5