Below are sample values iein cm obtained randomly from a pop

Below are sample values (i.e.in cm) obtained randomly from a population of 40 measurements of plant\'s stems. The population mean of the plant\'s stems is 21.525 (i.e. cm). Values of sample randomly selected are: 20, 28, 18, 19, 20,18, 22, 12, 6, 18, 37, 32,31, 14,28,33, 18,15, 22,18. Used the information given to answer the questions stated below: Find the sample mean, median, and mode, and find the sample variance and the sample standard deviation.

Solution

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    429      
As n =    20      
Thus,          
X =    21.45   [ANSWER, SAMPLE MEAN]  

Ordering the data,

6
12
14
15
18
18
18
18
18
19
20
20
22
22
28
28
31
32
33
37

Hence, the median is the average of the 10th and 11th entries,

Median = (19+20)/2 = 19.5 [ANSWER]

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Also, we can see that the mode is the most frequent observation,

Mode = 18 [ANSWER]

******************
          
Setting up tables,          
x   x - X   (x - X)^2  
20   -1.45   2.1025  
28   6.55   42.9025  
18   -3.45   11.9025  
19   -2.45   6.0025  
20   -1.45   2.1025  
18   -3.45   11.9025  
22   0.55   0.3025  
12   -9.45   89.3025  
6   -15.45   238.7025  
18   -3.45   11.9025  
37   15.55   241.8025  
32   10.55   111.3025  
31   9.55   91.2025  
14   -7.45   55.5025  
28   6.55   42.9025  
33   11.55   133.4025  
18   -3.45   11.9025  
15   -6.45   41.6025  
22   0.55   0.3025  
18   -3.45   11.9025  
          
          
Thus, Sum(x - X)^2 =    1158.95      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    20      
          
s^2 =    60.99736842   [ANSWER, SAMPLE VARIANCE]  
          
Thus,          
          
s =    7.810081205   [ANSWER, SAMPLE STANDARD DEVIATION]