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=i=1i=20xi20=0.8+...+4.920=60.720=3.035x=\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=x10+x112=3.1+3.92=3.5m={\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=i=1i=20(xix)220=(0.83.035)2+...+(4.93.035)220=27.3655201.368var=\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) σ=var=1.3681.170\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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