Let's find the average yield per plant and the standard deviation step by step.
### 1. Calculate the Average Yield
To find the average yield per plant, sum up the yields of all the plants and then divide by the number of plants.
The yields are: 4, 3.5, 4.5, 4.2, and 3.8.
First, sum these yields:
[tex]\[ 4 + 3.5 + 4.5 + 4.2 + 3.8 = 20.0 \][/tex]
There are 5 plants.
So, the average yield is:
[tex]\[ \text{Average Yield} = \frac{\text{Total Yield}}{\text{Number of Plants}} = \frac{20.0}{5} = 4.0 \][/tex]
### 2. Calculate the Standard Deviation
Standard deviation measures the amount of variation or dispersion in a set of values.
#### Step 1: Calculate the mean of the yields (already done)
[tex]\[ \text{Mean} = 4.0 \][/tex]
#### Step 2: Find the squared differences from the mean for each yield
For each yield, subtract the mean and square the result:
[tex]\[
(4 - 4.0)^2 = 0.0^2 = 0.0
\][/tex]
[tex]\[
(3.5 - 4.0)^2 = (-0.5)^2 = 0.25
\][/tex]
[tex]\[
(4.5 - 4.0)^2 = 0.5^2 = 0.25
\][/tex]
[tex]\[
(4.2 - 4.0)^2 = 0.2^2 = 0.04
\][/tex]
[tex]\[
(3.8 - 4.0)^2 = (-0.2)^2 = 0.04
\][/tex]
#### Step 3: Calculate the variance
The variance is the average of these squared differences:
[tex]\[
\text{Variance} = \frac{0.0 + 0.25 + 0.25 + 0.04 + 0.04}{5} = \frac{0.58}{5} = 0.116
\][/tex]
#### Step 4: Calculate the standard deviation
The standard deviation is the square root of the variance:
[tex]\[
\text{Standard Deviation} = \sqrt{0.116} \approx 0.34
\][/tex]
### Summary
Using the values calculated:
[tex]\[ \boxed{4.0} \][/tex]
[tex]\[ \boxed{0.34} \][/tex]
So, the average yield per plant is [tex]\( 4.0 \)[/tex] pints, and the standard deviation is [tex]\( 0.34 \)[/tex] pints.
