standard deviation

Question

Find the standard deviation of the data set. Round your answer to the nearest tenth.

3, 7, 10, 15, 26, 29

Answer 1

Re:standard deviation

Consider a data set consisting of the following six values: 3, 7, 10, 15, 26, 29 These six data points have the mean (average) of 6:  ( 3+7+10+15+26+29)/6=90/6=15 To calculate the data set standard deviation, first compute the difference of each data point from the mean, and square the result of each: (3-15)2=(-12)2=144 (7-15)2=(-8)2= 64 (10-15)2=(-5)2=25 (15-15)2=(0)2=0 (26-15)2=(11)2=121 (29-15)2=(14)2=196 Next compute the average of these values, and take the square root =√(144+64+25+0+121+196)/6 =√(550/6)  =√91.66 =9.57

 

Answer 2

Given numbers are 3 ,7 ,10 ,15 ,26 ,29

To  find  the mean

= 3+7+10+15+26+29 / 6

=90/6

=15

To caliculate the numbers  deviation  first  compute difference of each data point

from the mean ,and sqare the result of each.

(3-15)^2 = (-12)^2  = -12×(-12) =144

(7-15)^2  = (-8)^2  = -8×(-8) = 64

(10-15)^2 =(-5)^2  =-5×(-5) = 25

(15-15)^2 =(0)^2 = 0

(26-15)^2 = (11)^2 = 11×11 = 121

(29-15)^2 = (14)^2 = 14×14 =196

Next ,compute the mean of these values and take the square root.

= (144+64+25+0+121+196)/6

= 550/6

= 91.6

Square root of 91.6 is nearest to 9.5

Therefore the standerd deviation of the data set 3,7,10,15,26,29 is round to the nearest tenth is 9.