Answer to Question #264513 in Statistics and Probability for migs

Question #264513

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 


1
Expert's answer
2022-01-31T15:50:03-0500

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


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