Question

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: Plant 1 2 3 4 5 Yield 4 3.5 4.5 4.2 3.8 What is the average yield per plant, and what is the standard deviation (to two decimal places)?

Answer 1

Answer:

The average yield per plant is 20 and the standard deviation is 16.002

Step-by-step explanation:

Given: 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:

Plant      Yield

1                  4

2                 3.5

3                 4.5  

4                 4.2  

5                 3.8

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

Solution:

Average yield per plant = $\frac{\text{Sum of all yields}}{\text{Total no. of plants}}$

                                        = $\frac{4+3.5+4.5+4.2+3.8}{5}$

                                        = $20$

So, $\bar x =20$

Standard deviation=$\sigma = \sqrt{\frac{\sum (x-\bar x)^2}{n}}$

$\sigma = \sqrt{\frac{(4-20)^2+(3.5-20)^2+(4.5-20)^2+(4.2-20)^2+(3.8-20)^2}{5}}$

$\sigma = 16.003$

Hence the average yield per plant is 20 and the standard deviation is 16.002

Answer 2

The average is 4 and the standard deviation is 0.34. :)