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

Lets represent data in the increasing order

0.8, 1.1, 1.3, 1.8, 2.2, 2.4, 2.4, 2.4, 2.4, 3.1, 3.9, 3.9, 3.9, 3.9, 3.9, 4.0, 4.1, 4.1, 4.2, 4.9

a) Let x be mean, then

$x=\sum_{i=1}^{i=20}{\frac {x_i} {20}}={\frac {0.8+...+4.9} {20}}={\frac {60.7} {20}}=3.035$

b) sample size n = 20, then

$m={\frac {x_{10}+x_{11}} 2}={\frac {3.1+3.9} 2}=3.5$

c) number 3.9 is the most popular, then mo = 3.9

d) $var=\sum_{i=1}^{i=20}{\frac {(x_i-x)^2} {20}}={\frac {(0.8-3.035)^2+...+(4.9-3.035)^2} {20}}={\frac {27.3655} {20}}\approx1.368$

e) $\sigma=\sqrt{var}=\sqrt{1.368}\approx1.170$

f) minimum number is 0.8, maximum number is 4.9, then range

r = 4.9 - 0.8=4.1