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The standard deviations of four data sets are shown in the table below. Which
of the data sets is most spread out?
Data set
Standard deviation
5.21
Data set A
Data set B
4.88
Data set C
6.06
Data set D
3.39

A. Data set B
B. Data set D
C. Data set A
D. Data set C

Respuesta :

Answer:

[tex] s_A = 5.21[/tex]

[tex] s_B =4.88[/tex]

[tex] s_C = 6.06[/tex]

[tex]s_D =3.39[/tex]

We need to remember that the deviation is a measure od disperion and for this case is the deviation is larger then we have more spread out the distribution of interest. And largest deviation for this case is from the dataset C so then the answer would be:

D. Data set C

Step-by-step explanation:

For this case the standard deviation can be calculated with the following formula:

[tex] s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And for this case we have the deviations for each dataset are given by:

[tex] s_A = 5.21[/tex]

[tex] s_B =4.88[/tex]

[tex] s_C = 6.06[/tex]

[tex]s_D =3.39[/tex]

We need to remember that the deviation is a measure od disperion and for this case is the deviation is larger then we have more spread out the distribution of interest. And largest deviation for this case is from the dataset C so then the answer would be:

D. Data set C

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