Question

According to Chebyshev's Theorem, at least what proportion of the data will be within 1.7 standard deviation distance about the mean?

		95%
		91%
		81%
		72%
		65%

Compute the population variance of the data: 8, 7, 3, 1, 6.

		1.437
		3.871
		5.5
		6.8
		7.6

In a statistic class, 10 scores were randomly selected with the following results were obtained: 74, 73, 72, 72, 71, 68, 65, 66, 67, 66. What is the mode?

		66.0
		72.0
		77.0
		73.0
		None of the above

In a statistic class, 10 scores were randomly selected with the following results were obtained: 74, 73, 36, 60, 71, 68, 65, 77, 67, 98. What is the variance?

		92.72
		114.00
		204.72
		233.16
		237.88

Answer 1

• According to Chebycheb's inequality for a random variable with mean   :

or ,

Here k = 1.7 ,

SO, required answer is 65%

• Formula for population variance :

Here n =5   

So,

• Mode is the value occurring most frequently .

Here 72 and 66 both occurs twice . So both should be taken as mode.

• Here we are to calculate sample variance which is given by :

  

Here n = 10 and

So, sample variance =