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

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

Answer 2

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

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}}`

=
`(4+3.5+4.5+4.2+3.8)/(5)`

=
`20`

So,
`\bar x =20`

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

`\sigma = \sqrt{((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