Question

What is the sample variance of the following data, which describe the height growth of 10 foxtal pine trees grown in a common garden (give your answer to one decimal place)? Tree Height (cm)1 25 69872 19 65873 11.47804 9.111305 16.87476 1477717 33.00018 24 00009 19 444110 14 1010

Answer 1

Answer:

Although the data in the question is not clearly stated, the correct date is stated in the image attached to this answer and it is also stated below

What is the sample variance of the following data, which describe the height growth of 10 foxtail pine trees grown in a common garden ( give your  answer to one decimal place)?

Tree            Height(cm)

1                  25.6987

2                 19.6587

3                 11.4780

4                 9.11130

5                 16.8747

6                 14.7771

7                 33.0001

8                 24.0000

9                 19.4441

10                14.1010

answer 51.9

Explanation:

what is a sample variance?

A sample variance (denoted as $S^{2}$) is used to calculate how far a set of numbers are from the mean value of the set. Mathematically, it is defined as the average of the squared deviations from its mean value.

Let the individual value of the trees be represented as x₁ to x₁₀

Let the total number of Foxtail pine trees be N

To calculate the standard deviation, we will first calculate the mean or average of the height of the trees

1. Mean (μ) = $\frac{x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}+x_{7}+x_{8}+x_{9}+x_{10} }{N}$

                  = $\frac{25.6987+19.6587+11.4780+9.11130+16.8747+14.7771+33.0001+24.0000+19.4441+14.1010}{10}$  = $\frac{188.1437}{10} = 18.8144$

2. we need to calculate the sum of the squares of the individual deviations.

∑[x-μ]²= $(25.6987-18.8144)^{2}+(19.6587-18.8144)^{2}+(11.4780-18.8144)^{2}+(9.11130-18.8144)^{2}+(16.8747-18.8144)^{2}+(14.7771-18.8144)^{2}+(33.0001-18.8144)^{2}+(24.0000-18.8144)^{2}+(19.4441-18.8144)^{2}+(14.1010-18.8144)^{2}=466.8786$

3. Now the variance is ; (∑[x-μ]²) ÷ (N-1) and since N=10, then N-1 = 10-1 = 9

= $\frac{466.8786}{9} = 51.8754.$

we were asked the give our answer to one decimal place

∴ Variance($S^{2}$)= 51.9