Question

QUESTION 8

1. Two data sets that have the same range must also have the same standard deviation.

   True

   False

   QUESTION 9

2. It is possible to have a negative sample standard deviation (Hint: think about step 3 in the 6-step process.)

   True

   False

   QUESTION 10

3. When calculating for the following values, which calculation will use every value in the data set? (choose all that apply)

   	A.	Standard Deviation
   	B.	Mean
   	C.	Range
   	D.	Median QUESTION 11 Complete this definition: the standard deviation is a measure of how far individual values in a data set are away from..... A. Each other B. the mean C. the median QUESTION 12 Which of the following data sets would have a standard deviation of 0? A. -20, -10, 0, 10, 20 B. 0, 1, 2, 3, 4 C. 100, 150, 200, 250, 300 D. 5, 5, 5, 5, 5

Answer 1

solution:

8) False : If two data sets have same range no need to have same Standard Deviation.Because Range is the difference of largest and smallest value of a given data set.whereas Standard Deviation signifies how data much close (or) far away from mean within a given Data set.

Ex : Consider two data sets having same range

1) 2, 5, 7, 8, 12 Range = 12-2 = 10

2) 0, 1, 4, 5, 10 Range = 10-0 = 10

When you Calculate the mean and standard Deviation of 1 data set we get mean = 6.8 , S.D = √10.96

   When you Calculate the mean and standard Deviation of 2 data set we get mean = 4 , S.D = √12.4

Thus both Standard Deviations are different.

9) False:  Standard Deviation is always positive.Because, The formula for Standard Deviation is

Here, it's is the root over Total sum of square distance of each observation from mean divided by no.of observation.Squaring always gives us positive Standard Deviation.

10) Option A and B are correct: Because in  Calculating Mean and Standard Deviation

Mean =( X i ) / N  

S.D =

Xi - represents each observation value

But In calculating Range we only require smallest and largest data value and for median we require (n/2) th and sometimes (n/2)+1 th observations values.

11) B.The mean: The the definition of Standard Deviation is It's the measure of how far individual values in a data set are away from mean.Not median or each observation.

12) D.5,5,5,5,5 : Standard Deviation will be zero only when each and every observation of a given data set is equal to it's mean .

   Mean

A.-20,-10,0,10,20 0 [ mean value = 1 observation] - Incorrect

   B . 0,1,2,3,4 2    [ mean value = 1 observation] - Incorrect

C.100,150,200,250,300 200   [ mean value = 1 observation] -Incorrect

D.5,5,5,5,5 5    [ mean value = each observationvalue] -Correct