Question

Find standard deviation for: 2,3,5,2,7,5,7,6,11,12 *




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Answer 1

Step-by-step explanation:

Mean = sum of values / N (number of values in set)

Variance = ((n1- Mean)2 + ... nn- Mean)2) / N-1 (number of values in set - 1)

Standard Deviation σ = √Variance

Population Standard Deviation = use N in the Variance denominator if you have the full data set. The reason 1 is subtracted from standard variance measures in the earlier formula is to widen the range to "correct" for the fact you are using only an incomplete sample of a broader data set.

Answer 2

Answer:

Standard deviation of the data 2,3,5,2,7,5,7,6,11,12 =  $\sqrt{10.6}$

Step-by-step explanation:

Given data is 2,3,5,2,7,5,7,6,11,12

Required to find,

The standard deviation for: 2,3,5,2,7,5,7,6,11,12

Recall the concepts

Standard deviation is defined as square root of the mean of the square of the deviations of the each data from the the arithmetic mean

Solution:

Sum of observations  = 2+3+5+2+7+5+7+6+11+12

= 60

Total number of observations = 10

Hence mean of the data = 60/10 = 6

Deviations of observations from mean = 2-6, 3-6, 5-6,2-6,7-6,5-6,7-6,6-6,11-6,12-6

= -4,-3,-1,-4,1,-1,1,0,5,6

Square of deviations of observations from mean = 16+9+1+16+1+1+1+0+25+36

=  106

Mean of the squares of deviations of observations from mean = 106/10 = 10.6

Standard deviation = square root of mean of the squares of deviations of observations from mean   $\sqrt{10.6}$

Answer:

Standard deviation of the data 2,3,5,2,7,5,7,6,11,12 =  $\sqrt{10.6}$

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