standard deviation

Question

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

41, 44, 43, 39, 50, 54, 44, 46

Answer 1

Re:standard deviation

41, 44, 43, 39, 50, 54, 44, 46 Consider a population consisting of the following eight values: 41, 44, 43, 39, 50, 54, 44, 46 These eight data points have the mean (average) of 8: ( 41+ 44+ 43+39+ 50+ 54+ 44+ 46)/8=365/8=45.625 To    calculate the population standard deviation, first compute the    difference of each data point from the mean, and square the result of    each: (41-45.625)2=(-4.625)2=21.39 (44-45.625)2=(-1.625)2=2.64 (43-45.625)2=(-2.625)2=5.25 (39-45.625)2=(-6.625)2=43.89 (50-45.625)2=(5.625)2=31.64 (54-45.625)2=(-9.625)2=92.64 (44-45.625)2=(-1.625)2=2.64 (46-45.625)2=(1.625)2=2.64 Next compute the average of these values, and take the square root =√(21.39 +2.64+5.25+43.89+31.64+92.64+2.64+2.64)/8 =√(183.73/8) =√22.96625 =4.75

 

Answer 2

Given numbers are 41,44,43,39,50,54,44,46

Mean of these numbers =41+44+43+39+50+44+46+54/8

                                            =361/8

                                            =45

to find standerd devition set,first we find

      (41-45)^2=(-4)^2=16

     (44-45)^2=(-1)^2=1

    (43-45)^2=(-2)^2=4

   (39-45)^2=(-6)^2=36

   (5o-45)^2= (-5 )^2=25

   (54-45)^2=(-9)^2=81

(44-45)^2=(-1)^2=1

(46-45)^2=(1)^2=1

mean=16+1+4+36+25+81+1+1/8

          =165/8

         =20.6

Standard davition=

Comments

The standard deviation is 4.75.