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
(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
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