Respuesta :
By using the formula for mean and standard deviation, it can be concluded that
For list A and list B,
The mean are same and the standard deviation are different.
First option is correct
What is mean and standard deviation?
Mean is the average of all the values of a data set.
To know about standard deviation, it is important to know about variance
Variance is the sum of the square of deviation from mean divided by the number of observation
Square root of the variance is the standard deviation.
For list A
Mean = [tex]\frac{1 +2+3+4+5+6}{6}[/tex]
= 3.5
Variance = [tex]\frac{(1-3.5)^2 + (2 -3.5)^2+ (3 - 3.5)^2 + (4 - 3.5)^2+(5 - 3.5)^2+(6 - 3.5)^2}{6}[/tex]
= [tex]\frac{6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25}{6}[/tex]
= 17.5
Standard deviation = [tex]\sqrt{17.5} = 4.18[/tex]
For list B
Mean = [tex]\frac{2 + 3 + 3 + 4 + 4 +5}{6}[/tex]
= 3.5
Variance = [tex]\frac{(2-3.5)^2 + (3 -3.5)^2+ (3 - 3.5)^2 + (4 - 3.5)^2+(4 - 3.5)^2+(5 - 3.5)^2}{6}[/tex]
= [tex]\frac{2.25 + 0.25 + 0.25 + 0.25 + 0.25 + 2.25}{6}[/tex]
= 0.916
Standard deviation = [tex]\sqrt{0.916}[/tex] = 0.957
To learn more about mean and standard deviation, refer to the link-
https://brainly.com/question/26941429
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