Answer:
The mean is 87.43.
The standard derivation is 28.11.
Step-by-step explanation:
If we multiply each number by three, we have:
19*3 = 57
23*3 = 69
25*3 = 75
27*3 = 81
30*3 = 90
32*3 = 96
48*3 = 144
First, let's calculate the mean:
The means (x) is found by adding up the values and then dividing by the number of values that you added.
x = (57+69+75+81+90+96+144)/7
x = 87.42
The mean is 87.43.
Now, let's calculate the standard derivation of the sample:
The standard derivation (s) can be estimated as follows:
![s=\sqrt[]{(\sum ^n_(i\mathop=1)(x_i-x)^2)/(n-1)}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/vyqkifas3ui3z37kpsa9.png)
Where n is the number of the samples, xi are the values of the samples (57, 69, ...) and x is the mean.
In this exercise, we have:
![\begin{gathered} s=\sqrt[\square]{((57-87.43)^2+(69-87.43)^2+(75-87.43)^2+(81-87.43)^2+(90-87.43)^2+(96-87.43)^2+(144-87.43)^2)/(7-1)} \\ s=\sqrt[]{790.29} \\ s=28.11 \end{gathered}]()
The standard derivation is 28.11.