Question

Consider the following two data sets. Data Set I: 12 25 37 8 4 Data Set 11: 26 39 51 22 55 Note that each value of the second data set is obtained by adding 14 to the corresponding value of the first data set. Calculate the standard deviation for each of these two data sets using the formula for sample data. Round your answers to two decimal places. Standard deviation of Data Set 1 Standard deviation of Data Set II

Answer 1

Answer:

$\bar X_I =\frac{12+25+37+8+41}{5}=24.6$

$\bar X_{II} =\frac{26+39+51+22+55}{5}=38.6$

And then we can calculate the standard deviation with the following formula:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$s_I = \sqrt{\frac{(12-24.6)^2 +(25-24.6)^2 +(37-24.6)^2 +(8-24.6)^2 +(41-24.6)^2}{5-1}}= 14.639$

$s_{II} = \sqrt{\frac{(26-38.6)^2 +(39-38.6)^2 +(51-38.6)^2 +(22-38.6)^2 +(55-38.6)^2}{5-1}}=14.639$

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:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X_I =\frac{12+25+37+8+41}{5}=24.6$

$\bar X_{II} =\frac{26+39+51+22+55}{5}=38.6$

And then we can calculate the standard deviation with the following formula:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$s_I = \sqrt{\frac{(12-24.6)^2 +(25-24.6)^2 +(37-24.6)^2 +(8-24.6)^2 +(41-24.6)^2}{5-1}}= 14.639$

$s_{II} = \sqrt{\frac{(26-38.6)^2 +(39-38.6)^2 +(51-38.6)^2 +(22-38.6)^2 +(55-38.6)^2}{5-1}}=14.639$

So as we can see both deviations are the same, the only thing that change is the mean.