Answer to Question #262616 in Statistics and Probability for Matheca

Question

The College of Agriculture obtained the following data representing the one-week growth in centimeters of 20

newly planted soybean plants:

1.3

4.9

3.9

0.8

4.1

1.1

3.1

2.2

2.4

2.4

2.4

3.9

1.8

3.9

3.9

4.1

3.9

2.4

4.0

4.2

Find the following:

a. Mean 

b. Median 

c. Mode 

d. Variance 

e. Standard Deviation 

f. Range 

Answer 1

(a) Mean

$Mean = \frac{\Sigma X}{N}$

$= \frac{(1.3+4.9+3.9+0.8+4.1+1.1+3.1+2.2+2.4+2.4+2.4+3.9+1.8+3.9+3.9+4.1+3.9+2.4+4.0+4.2)}{20}$

$= \frac{60.7}{20}=3.035$

(b) Median

$Median = \frac{(\frac{n}{2})term+(\frac{n}{2}+1)term}{2}$

Firstly need to arrange data in ascending order like below:

$Median = \frac{(\frac{20}{2})term+(\frac{20}{2}+1)term}{2}=\frac{3.1+3.9}{2}$

Median = 3.5

(c) Mode

Mode represents the number of observations in a data set that is occurring most of the time. As shown in above table, 3.9 is occurring 5 times in the data set. This mean mode is 3.9 in case of given data set.

(d) Variance

$s^{2}=\frac{\varSigma (X-Mean)^{2}}{n-1}$

$s^{2}=\frac{27.37}{20-1}=1.44029$

(e) Standard Deviation

$s= \sqrt{Variance}=\sqrt{1.44029}=1.20012$

(f) Range

Range = Maximum - Minimum

Range = 4.2 - 1.3 = 2.9