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
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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