A homeowner has 5 cherry tomato plants in her garden. Over the course of the season, the yields (in pints of tomatoes per plant) are:

[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Plant & 1 & 2 & 3 & 4 & 5 \\
\hline
Yield & 4 & 3.5 & 4.5 & 4.2 & 3.8 \\
\hline
\end{tabular}
\][/tex]

What is the average yield per plant, and what is the standard deviation (to two decimal places)?

Average: [tex]$\square$[/tex]

Standard Deviation: [tex]$\square$[/tex]



Answer :

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.