Homework Sourseinformation2 below are measurements of plants stem of of a f
information#2 below are measurements of plants stem of of a flower plant population in the botanys garden. the population consists of 40 plants and their measurement values are as follows:20,28,18,19,20,18,22,12,6,18,37,32,31,14,28,33,18,15,22,18,7,33,28,15,16,13,28,25,17,20,24,19,11,33,16,23,28,27.
use the information given above to answer the questions below.
find the population mean,and the population variance and the standard deviation
Solution
3a)
Getting the mean, u,
u = Sum(x) / n
Summing the items, Sum(x) = 861
As n = 40
Thus,
u = 21.525 [ANSWER, POPULATION MEAN]
Setting up tables,
x x - u (x - u)^2
20 -1.525 2.325625
28 6.475 41.925625
18 -3.525 12.425625
19 -2.525 6.375625
20 -1.525 2.325625
18 -3.525 12.425625
22 0.475 0.225625
12 -9.525 90.725625
6 -15.525 241.025625
18 -3.525 12.425625
37 15.475 239.475625
32 10.475 109.725625
31 9.475 89.775625
14 -7.525 56.625625
28 6.475 41.925625
33 11.475 131.675625
18 -3.525 12.425625
15 -6.525 42.575625
22 0.475 0.225625
18 -3.525 12.425625
7 -14.525 210.975625
33 11.475 131.675625
28 6.475 41.925625
15 -6.525 42.575625
16 -5.525 30.525625
13 -8.525 72.675625
28 6.475 41.925625
25 3.475 12.075625
17 -4.525 20.475625
20 -1.525 2.325625
24 2.475 6.125625
19 -2.525 6.375625
11 -10.525 110.775625
33 11.475 131.675625
16 -5.525 30.525625
23 1.475 2.175625
28 6.475 41.925625
21 -0.525 0.275625
28 6.475 41.925625
27 5.475 29.975625
Thus, Sum(x - u)^2 = 2167.975
Thus, as
sigma^2 = Sum(x - u)^2 / n
As n = 40
sigma^2 = 54.199375 [ANSWER, POPULATION VARIANCE]
Thus,
sigma = 7.36202248 [ANSWER, POPULATION STANDARD DEVIATION]
