Question

Which of the following sets of data has the same standard deviation as

38, 39, 40, 41?

. 2, 3, 4, 5

. 2, 2, 3, 3

. 0, 0, 10, 10

. 2, 2, 2, 2

Answer 1

We assume the data set is a sample. Let be the mean of the data. The standard deviation of the data set is given by

data-38,39,40,41 Here n=4. Mean=(38+39+40+41)/4= 39.5

Now,

  

data set 1: 2,3,4,5

here mean=(2+3+4+5)/4= 3.5

  

data set 2: 2,2,3,3

here mean=(2+2+3+3)/4= 2.5

data set 3: 0,0,10,10

here mean=(0+0+10+10)/4= 5

data set 3: 2,2,2,2

here mean=(2+2+2+2)/4= 2

  

hence data set 1 has same standard deviation as the given set.