Respuesta :
Answer:
[tex]\bar X_I =\frac{12+25+37+8+41}{5}=24.6 [/tex]
[tex]\bar X_{II} =\frac{26+39+51+22+55}{5}=38.6 [/tex]
And then we can calculate the standard deviation with the following formula:
[tex] s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex] s_I = \sqrt{\frac{(12-24.6)^2 +(25-24.6)^2 +(37-24.6)^2 +(8-24.6)^2 +(41-24.6)^2}{5-1}}= 14.639[/tex]
[tex] s_{II} = \sqrt{\frac{(26-38.6)^2 +(39-38.6)^2 +(51-38.6)^2 +(22-38.6)^2 +(55-38.6)^2}{5-1}}=14.639 [/tex]
So as we can see both deviations are the same, the only thing that change is the mean.
Step-by-step explanation:
For this case we have the following data given:
Data Set I: 12 25 37 8 41
Dataset II: 26 39 51 22 55
And for this case we want to calculate the deviation for each dataset.
First we need to calculate the sample mean for each dataset with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X_I =\frac{12+25+37+8+41}{5}=24.6 [/tex]
[tex]\bar X_{II} =\frac{26+39+51+22+55}{5}=38.6 [/tex]
And then we can calculate the standard deviation with the following formula:
[tex] s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex] s_I = \sqrt{\frac{(12-24.6)^2 +(25-24.6)^2 +(37-24.6)^2 +(8-24.6)^2 +(41-24.6)^2}{5-1}}= 14.639[/tex]
[tex] s_{II} = \sqrt{\frac{(26-38.6)^2 +(39-38.6)^2 +(51-38.6)^2 +(22-38.6)^2 +(55-38.6)^2}{5-1}}=14.639 [/tex]
So as we can see both deviations are the same, the only thing that change is the mean.
